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This study aimed to quantify in- and between-match characteristics and mechanical workload variations elicited by a congested schedule in high-level female ice hockey. Six players were monitored during four international pre-season exhibition matches against the same opponent. Two different methods (Player Load and Accel'Rate) were used to assess specific mechanical workload. Number of shifts and effective playing time per shift were significantly higher for period 2 (p = 0.03 for both). Mechanical workload intensity (i.e., relative and peak workload) showed a significant (p ≤ 0.05) decrease from period 1 to period 2 and period 3 (

International audience; Agroforestry consists of combining trees with agriculture, both on farms and in the agricultural landscape. Within a context of sustainable development, agroforestry can improve soil conservation and reduce the use of toxic chemicals on crops, as well as improving biodiversity. Interdisciplinary by nature, the field of agroforestry mobilizes a large body of knowledge from environmental and life sciences using systemic approaches. In this framework, field observation data are acquired in partnership with several categories of stakeholders such as scientists, foresters, farmers, breeders, politicians and land managers. For data management effciency, we propose the software application AOBRA (a softwareApplication with Ontology-Based Reasoning for Agroforestry). The core of AOBRA is a domain ontology called "Agroforestry" which serves as a basis for capitalizing and sharing knowledge in agroforestry. By exploiting the capabilities of inference and linkages to other areas of expertise on the Web offered by the use of an ontology model, it aims to provide a broad view of agroforestry designs, and to allow the comparison between different spatial layouts of trees and crops

Isochrone potentials, as defined by Michel H\'enon in the fifties, are spherically symmetric potentials within which a particle orbits with a radial period that is independent of its angular momentum. Isochrone potentials encompass the Kepler and harmonic potential, along with many other. In this article, we revisit the classical problem of motion in isochrone potentials, from the point of view of Hamiltonian mechanics. First, we use a particularly well-suited set of action-angle coordinates to solve the dynamics, showing that the well-known Kepler equation and eccentric anomaly parametrisation are valid for any isochrone orbit (and not just Keplerian ellipses). Second, by using the powerful machinery of Birkhoff normal forms, we provide a self-consistent proof of the isochrone theorem, that relates isochrone potentials to parabolae in the plane, which is the basis of all literature on the subject. Along the way, we show how some fundamental results of celestial mechanics such as the Bertrand theorem and Kepler's third law are naturally encoded in the formalism., Comment: 36 pages, 5 figures, 1 table

International audience; The aims of this study were to ensure that the skating velocity describes a mono-exponential function in order to determine the reliability of radar-derived profiling results from skating sprint accelerations applying sprint running force-velocity assessment approach. Eleven young highly-trained female ice hockey players performed two 40-m skating sprints on two separate days to evaluate inter-trial and test-retest reliability. The velocity-time data recorded by a radar device was used to calculate the kinetics variables of the skating sprint acceleration: maximal theoretical force (F0), maximal theoretical velocity (V0), maximal theoretical power (Pmax) and the slope of the linear force-velocity relationship (SFV). SFV and SFVrel variables (the slope of the linear relationship between horizontal force relative to body mass and velocity) demonstrated ‘low’ to ‘moderate’ intra-class correlation coefficients (ICC). All other variables revealed ‘acceptable’ inter-trial and testretest reliability (ICC ≥ 0.75 and coefficient of variation [CV] ≤ 10%). Furthermore, test-retest reliability (ICC and CV) and sensitivity [Standard Error of Measurement (SEMs) ≤ Small Worthwhile Change (SWCs)] were higher when averaging the two trials compared to the best trial (40-m split time) only. These findings offer a promising and simple method to monitor training-induced changes in macroscopic mechanical variables of ice hockey skating performance.

In classical mechanics, the Kepler potential and the Harmonic potential share the following remarkable property: in either of these potentials, a bound test particle orbits with a radial period that is independent of its angular momentum. For this reason, the Kepler and Harmonic potentials are called \it{isochrone}. In this paper, we solve the following general problem: are there any other isochrone potentials, and if so, what kind of orbits do they contain? To answer these questions, we adopt a geometrical point of view initiated by Michel H\'enon in 1959, in order to explore and classify exhaustively the set of isochrone potentials and isochrone orbits. In particular, we provide a geometric generalization of Kepler's third law, and give a similar law for the apsidal angle, for any isochrone orbit. We also relate the set of isochrone orbits to the set of parabolae in the plane under linear transformations, and use this to derive an analytical parameterization of any isochrone orbit. Along the way we compare our results to known ones, pinpoint some interesting details of this mathematical physics problem, and argue that our geometrical methods can be exported to more generic orbits in potential theory., Comment: 54 pages, 18 figures

In the potential theory, isochrony was introduced by Michel H\'enon in 1959 to characterize astrophysical observations of some globular clusters. Today, Michel Henon's isochrone potential is mainly used for his integrable property in numerical simulations, but is generally not really known. In a recent paper [29], we have presented new fundamental and theoretical results about isochrony that have particular importance in self-gravitating dynamics and which are detailed in this paper. In particular, new characterization of the isochrone state has been proposed which are investigated in order to analyze the product of the fast relaxation of a self-gravitating system. The general paradigm consists in considering that this product is a lowered isothermal sphere (King Model). By a detailed numerical study we show that this paradigm fails when the isochrone model succeeds in reproducing the quasi-equilibrium state obtained just after fast relaxation., Comment: 23 pages, 7 figures, 1 table, accepted for publication in MNRAS

Purpose:To evaluate the effects of muscle fatigue on badminton performance during a smash stroke.Methods:In total, 17 young, well-trained players completed 20 forehand smashes twice (prefatigue and postfatigue protocol), and both speed and precision of the strokes were measured. The fatigue protocol consisted of 10 series of 10 maximal countermovement jumps (3-s rest in between) followed by 8 lunges. Perception of effort and countermovement-jump performance during each series were also measured to assess fatigue.Results:Shuttlecock speed decreased moderately (−3.3%) but significantly after the fatigue protocol (P ). Precision significantly decreased after the fatigue protocol (−10.3%,P = .001,). The decrease in precision was mainly due to an increased number of faults (P = .006,,dz = 0.756) and to a decrease in accuracy (P = .066,,dz = 0.478).Conclusion:The present study showed that fatigue impairs performance during specific badminton skills. Moreover, by showing a slight decrease in speed and a large decrease in accuracy of the shuttlecock when fatigue is experienced, the present study suggested that, as previously observed in other racket sports, the speed of the missile appears to be the key factor used by the players to win the rally. Coaches and physical trainers should therefore develop interventions aiming to limit the negative impact of fatigue on badminton strokes.

Revisiting and extending an old idea of Michel H\'enon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in potential theory. They appear in spherically symmetrical systems formed by a large amount of charges (electrical or gravitational) of the same type considered in mean-field theory. Such potentials are defined by the fact that the radial period of a test charge in such potentials, provided that it exists, depends only on its energy and not on its angular momentum. Our characterization of the isochrone set is based on the action of a real affine subgroup on isochrone potentials related to parabolas in the $\mathbb{R}^2$ plane. Furthermore, any isochrone orbits are mapped onto associated Keplerian elliptic ones by a generalization of the Bohlin transformation. This mapping allows us to understand the isochrony property of a given potential as relative to the reference frame in which its parabola is represented. We detail this isochrone relativity in the special relativity formalism. We eventually exploit the completeness of our characterization and the relativity of isochrony to propose a deeper understanding of general symmetries such as Kepler's Third Law and Bertrand's theorem., Comment: 67 pages, 7 theorems, 6 lemmas, 4 propositions and 2 corrolaries

International audience; We confront stability results over long time scales, considering alternately the averagedand the non-averaged theory to propagate the equations of motion of a celestial bodyorbiting the vicinity of the (2:1) tesseral resonant surface. This confrontation is performedusing Fast Lyapunov Indicator stability maps. The benefit of such maps is threefold: (i) toreveal the whole phase space architecture and the consequences of the resonance overlapwhen several combinations of tesseral resonant parameters are accounted for, (ii) toperform a stability analysis on a whole phase space region, and (iii) to have a clear view ofthe possible impacts of the short-periodic effects removed during the averaging procedure.Our detailed numerical investigations conclude that the tesseral chaos is robust tothe averaging procedure and the numerical methods used to propagate the equations ofmotion over such long time scales.

Due largely to anthropogenic activities and extreme climate events, the risk of shallow landslides and erosion has increased enormously over the last decade. Although the planting of vegetation is widely acknowledged as improving soil conservation on slopes, how to plant and manage a vegetated slope over time can be problematic. Correct identification of the mass-wasting process and site characterization is necessary before choosing the plant species best suited to a site. To aid the site manager choose the most appropriate species, we have developed a database containing species sorted by their utility for retaining soil on slopes subject to shallow landslides, wind and water erosion. The list of species was compiled from the literature and suitability is based on ecological attributes, shoot and root traits. The database is open to experts who can add new information via a website, whereas the general public can access the data freely: http://publish.plantnet-project.org/project/stability_en.

Among the most pressing threats to the global coffee trade are a widening gap between supply and demand, an exodus of young farmers, and the impact of climate change. If these and other factors, including economic volatility, are simply ignored, the industry faces a challenging future. This chapter uses the price , cost , and value of coffee as distinct but connected lenses to engender a deeper understanding of the economic challenges facing the sector. Taking this holistic view helps to emphasize how an obsession with price (at all levels of the value chain) is inhibiting improvement by relegating coffee to the status of a mere commodity. Although there is no panacea for the many challenges, we offer solutions built on data and models of economic theory. We aim to provoke both thought and action, advocating multilevel assistance to level the playing field for farmers trapped by systems that are failing, whereas trusting in the power of strong value propositions to foster innovation at the producer level. This chapter argues that solutions that truly work are likely to come from a shared belief in the creation of shared value . This chapter includes analyses from Fairtrade senior managers, global sustainability experts, and the son of a Colombian coffee farmer. To survive, the coffee industry must draw on its greatest asset—the creativity, entrepreneurship, and drive that exist from the bottom to the top of its unique and remarkable value chain.

The influence of vegetation on slope stability is well understood at the slope level but scaling up to the catchment level is still a challenge, partially because of a lack of suitable data to validate models. We tested the physical landslide model, LAPSUS_LS, which models slope stability at the catchment scale. LAPSUS_LS combines a hydrological model with a Limit Equilibrium Method model, and calculates the factor of safety of individual cells based on their hydrological and geomorphological characteristics. We tested two types of vegetation on slope stability: (i) coffee monoculture (Coffea arabica) and (ii) a mixed plantation of coffee and deep rooting Erythrina (Erythrina poeppigiana) trees. Using soil and root data from Costa Rica, we performed simulations to test the response of LAPSUS_LS to root reinforcement, soil bulk density, transmissivity, internal friction angle and depth of shear plane. Furthermore, we modified the model to include biomass surcharge effect in the calculations. Results show that LAPSUS_LS was most sensitive to changes in additional cohesion from roots. When the depth of the shear plane was fixed at 1.0 m, slopes were not unstable. However, when the shear plane was fixed to 1.5 m, the mixed plantation of coffee and trees stabilized slopes, but the coffee monoculture was highly unstable, because root reinforcement was low at a depth of 1.5 m. Soil transmissivity had a limited impact on the results compared to bulk density and internal friction angle. Biomass surcharge did not have any significant effect on the simulations. In conclusion, LAPSUS_LS responded well to the soil and vegetation input data, and is a suitable candidate for modeling the stability of vegetated slopes at the catchment level.

The risk of shallow landslides and erosion has increased enormously over the last decade, often due to poor management or a lack of understanding of basic soil instability processes. Although the planting of vegetation is widely acknowledged as improving soil conservation on slopes, how to plant and manage a vegetated slope over time can be problematic. Correct identification of the mass-wasting process and site characterization is necessary before choosing the plant species best suited to a site. To aid the site manager choose the most appropriate species, we have developed an open access database ‘Stability,’ containing species sorted by their utility for retaining soil on slopes subject to shallow landslides, wind and water erosion. The list of species was compiled from the literature and suitability is based on ecological attributes, shoot and root traits. The database is open to experts who can add new information via a website, whereas the general public can access the data freely: http://publish.plantnet-project.org/project/stability_en

The risk of shallow landslides and erosion has increased enormously over the last decade, often due to poor management or a lack of understanding of basic soil instability processes. Although the planting of vegetation is widely acknowledged as improving soil conservation on slopes, how to plant and manage a vegetated slope over time can be problematic. Correct identification of the mass-wasting process and site characterization is necessary before choosing the plant species best suited to a site. To aid the site manager choose the most appropriate species, we have developed an open access database ‘Stability,’ containing species sorted by their utility for retaining soil on slopes subject to shallow landslides, wind and water erosion. The list of species was compiled from the literature and suitability is based on ecological attributes, shoot and root traits. The database is open to experts who can add new information via a website, whereas the general public can access the data freely: http://publish.plantnet-project.org/project/stability_en

In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case appearing as a special case of this larger framework. Then, depending on the rationality of the Kovalewski exponents, the different models, both in the vacuum and in presence of a barotropic matter fluid, are classified, and their integrability is discussed., Comment: 16 pages, no figure, accepted in CQG

We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting incomplete violent relaxation. Within a combinatorial analysis similar to that of Lynden-Bell, we make use of this association to obtain a distribution function that deviates from the Maxwell-Boltzmann distribution, increasing its slope for high energies. Considering the smallness of the occupation numbers for large distances from the center of the system, we apply a correction to Stirling's approximation which increases the distribution slope also for low energies. The distribution function thus obtained presents some resemblance to the "S" shape of distributions associated with cuspy density profiles (as compared to the distribution function obtained from the Einasto profile), although it is not quite able to produce sharp cusps. We also argue how the association between mixing level and indistinguishability can provide a physical meaning to the assumption of particle-permutation symmetry in the N-particle distribution function, when it is used to derive the one-particle Vlasov equation, which raises doubts about the validity of this equation during violent relaxation., Minor changes; Published in PRD

In this paper, we exploit the fact that the dynamics of homogeneous andisotropic Friedmann–Lemaître universes is a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling theUniverse. Without coupling between those fluids, Lotka–Volterra formulation offersa pedagogical and simple way to interpret usual Friedmann–Lemaître cosmologicaldynamics. A natural and physical coupling between cosmological fluids is proposedwhich preserves the structure of the dynamical equations. Using the standard toolsof Lotka–Volterra dynamics, we obtain the general Lyapunov function of the systemwhen one of the fluids is coupled to dark energy. This provides in a rigorous forma generic asymptotic behavior for cosmic expansion in presence of coupled species,beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, weconjecture that chaos can appear for at least four interacting fluids.

ObjetivoInvestigar los rasgos de personalidad que podrían asociarse con puntuaciones altas en las escalas de burnout (Maslach Burnout Inventory) en médicos de atención primaria.DiseñoEstudio observacional, descriptivo, transversal.EmplazamientoNoventa y tres centros de atención primaria de la ciudad de Barcelona y las comarcas del norte de la provincia: Vallès Oriental, Vallès Occidental, Maresme, Osona, Bages y Berguedà (región sanitaria centro).MétodoEncuesta directa por entrevista personal o grupal a 528 médicos de atención primaria. Se administraron 3 cuestionarios: uno de datos sociodemográficos generales, el Maslasch Burnout Inventory (MBI) y el test de personalidad de Cattell 16 PF-5.ResultadosUn 40% de los encuestados presentaba algún síntoma de burnout sin diferencia entre sexos. De éstos, un 12,4% manifestaba niveles muy altos de «quemazón» profesional. Los sujetos con criterios de burnout obtuvieron puntuaciones significativamente diferentes en los rasgos de estabilidad, tensión y vigilancia y en la dimensión ansiedad.ConclusionesAlgunos rasgos de personalidad, como la baja estabilidad emocional, la tensión y la ansiedad, se asocian de manera significativa a puntuaciones altas de burnoutExisten algunas diferencias entre estos factores internos por sexo.ObjectiveWith this research we try to study personality traits that could be associated with high punctuation at burnout scales (Maslach Burnout Inventory) in primary care physicians.DesignObservational descriptive transversal studySetting93 primary care centres in Barcelona-city and the northern province's region: Vallès Oriental, Vallès Occidental, Maresme, Osona, Bages and Berguedà (centre sanitary region).MethodIndividual or collective direct interview to 528 primary care physicians. Three questioners were administrated: a sociodemographyc items one, the Maslach Burnout Inventory (MBI) and the Cattell personality test 16-PF.ResultsThe 40% of the interviewed physicians had some burnout symptom without any difference between sexes. The 12.4% of these ones showed very high burnout levels. Those subjects with burnout criteria punctuated different at stability, tension and vigilance traits and anxiety dimension.ConclusionSome personality traits like low stability, the tension and the anxiety are associated with high punctuation of burnout.

We report on analysis of 308.3 hrs of high speed photometry targeting the pulsating DA white dwarf EC14012-1446. The data were acquired with the Whole Earth Telescope (WET) during the 2008 international observing run XCOV26. The Fourier transform of the light curve contains 19 independent frequencies and numerous combination frequencies. The dominant peaks are 1633.907, 1887.404, and 2504.897 microHz. Our analysis of the combination amplitudes reveals that the parent frequencies are consistent with modes of spherical degree l=1. The combination amplitudes also provide m identifications for the largest amplitude parent frequencies. Our seismology analysis, which includes 2004--2007 archival data, confirms these identifications, provides constraints on additional frequencies, and finds an average period spacing of 41 s. Building on this foundation, we present nonlinear fits to high signal-to-noise light curves from the SOAR 4.1m, McDonald 2.1m, and KPNO 2m telescopes. The fits indicate a time-averaged convective response timescale of 99.4 +/- 17 s, a temperature exponent 85 +/- 6.2 and an inclination angle of 32.9 +/- 3.2 degrees. We present our current empirical map of the convective response timescale across the DA instability strip., Comment: Accepted for publication in the Astrophysical Journal

This paper is devoted to Radial Orbit Instability in the context of self-gravitating dynamical systems. We present this instability in the new frame of Dissipation-Induced Instability theory. This allows us to obtain a rather simple proof based on energetics arguments and to clarify the associated physical mechanism.

This paper presents elements about the radial orbit instability, which occurs in spherical self-gravitating systems with a strong anisotropy in the radial velocity direction. It contains an overview on the history of radial orbit instability. We also present the symplectic method we use to explore stability of equilibrium states, directly related to the dissipation induced instability mechanism well known in theoretical mechanics and plasma physics., Comment: 10 pages, submitted to Transport Theory and Statistical Physics, proceedings of Vlasovia 2009 International Conference. Corrected for typos, redaction, and references added

This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson model to the astrophysical systems like globular clusters or galaxies. In a second part we will recall some recent numerical results which may give us some some quantitative hints about the equilibrium state associated to those systems., Comment: 8 pages, no figures, accepted in Communications in Nonlinear Science and Numerical Simulation

Is it actually possible to interpret gravitation as space's property in a pure classical way. Then, we note that extended self-gravitating system equilibrium depends directly on the number of dimension of the space in which it evolves. Given those precisions, we review the principal thermodynamical knowledge in the context of classical gravity with arbitrary dimension of space. Stability analyses for bounded 3D systems, namely the Antonov instability paradigm, are then rapproched to some amazing properties of globular clusters and galaxies., Comment: 11 pages, 3 figures, proceedings of the international workshop "Statistical Mechanics of Non-Extensive Systems" held in Paris Observator, 24-25 October 2005. to be published in a special issue of "Les Comptes rendus de l'Academie des science"

We present a general study of the dynamical properties of Anisotropic Bianchi Universes in the context of Einstein General Relativity. Integrability results using Kovalevskaya exponents are reported and connected to general knowledge about Bianchi dynamics. Finally, dynamics toward singularity in Bianchi type VIII and IX universes are showed to be equivalent in some precise sence., Comment: 12 pages, 6 figures, Proceedings of the Albert Einstein Century International Conference, held in Paris, France, July 18-22, 2005. to be published in AIP

We present Vlasov's equation and its association with Poisson's equation in the context of modelling self-gravitating systems such as Globular Clusters or Galaxies. We first review the classical hypotheses of the model. We continue with a presentation of the Hamilton-Morrison structure of Vlasov's equation to study the equilibrium and the stability of self-gravitating systems. Finally, we present some preliminary results concerning some properties of the time dependent solutions of the Vlasov-Poisson system., Comment: 13 pages, no figures, Review paper presented in First International Workshop on the Theory and Applications of the Vlasov Equation, Nancy, France, November 2003, to appear in a special issue of in a special issue of "Transport Theory and Statistical Physics"

International audience; We present a new approach to deal with the problem of stability of collisionless stelar systems. This technique based on the symplectic struc-ture of the Vlasov-Poisson system allow us to have a new stability criteria for general systems very usefull in the anisotropic spherical case.

International audience; The thermodynamics of a two-dimensional self-gravitating system occupying the whole plane is considered in the mean-field approximation. First, it is proven that, if the number N of particles and the total energy E are imposed as the only external constraints, then the entropy admits the least upper bound S+(N,E)=2E/N+N ln(eπ2) (in appropriate units). Moreover, there does exist a unique state of maximum entropy, which is characterized by a Maxwellian distribution function with a temperature T=N/2 independent of E. Next, it is shown that, if the total angular momentum J is imposed as a further constraint, the largest possible value of the entropy does not change, and there is no admissible state of maximum entropy, but in the case J=0. Finally, some inequalities satisfied by a class of so-called H functions and related generalized entropies are given.

We study the stability of rotating collisionless self-gravitating spherical systems by using high resolution N-body experiments on a Connection Machine CM-5. We added rotation to Ossipkov-Merritt (hereafter OM) anisotropic spherical systems by using two methods. The first method conserves the anisotropy of the distribution function defined in the OM algorithm. The second method distorts the systems in velocity space. We then show that the stability of systems depends both on their anisotropy and on the value of the ratio between the total kinetic energy and the rotational kinetic energy. We also test the relevance of the stability parameters introduced by Perez et al. (1996) for the case of rotating systems., 15 Pages, 5 Figures, accepted for publication in MNRAS

The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically symmetric, and its distribution function $f_0$ thus depends only on the energy $E$ and the squarred angular momentum $L^2$ of a particle. Assuming that $\partial f_0 / \partial E < 0$, it is first shown that stability holds with respect to all the spherical perturbations -- a statement which turns out to be also valid for a rotating spherical system. Thus it is proven that the energy of an arbitrary aspherical perturbation associated to a ``preserving generator" $\delta g_1$ [i.e., one satisfying $\partial f_0 / \partial L^2 \{ \delta g_1, L^2 \} = 0$] is always positive if $\partial f_0 / \partial L^2 \leq 0$ and the external mass density is a decreasing function of the distance $r$ to the center. This implies in particular (under the latter condition) the stability of an isotropic system with respect to all the perturbations. Some new remarks on the relation between the symmetry of the system and the form of $f_0$ are also reported. It is argued in particular that a system with a distribution function of the form $f_0 = f_0 (E,L^2)$ is necessarily spherically symmetric., Comment: uuencoded compressed postscript file containing 13 pages, accepted for publication in MNRAS

We have performed a series of high resolution N-body experiments on a Connection Machine CM-5 in order to study the stability of collisionless self-gravitating spherical systems. We interpret our results in the framework of symplectic mechanics, which provides the definition of a new class of particular perturbations: The preserving perturbations, which are a generalization of the radial ones. Using models defined by the Ossipkov-Merritt algorithm, we show that the stability of a spherical anisotropic system is directly related to the preserving or non-preserving nature of the perturbations acting on the system. We then generalize our results to all spherical systems. Since the ``isotropic component'' of the linear variation of the distribution function cannot be used to predict the stability or instability of a spherical system, we propose a more useful stability parameter which is derived from the ``anisotropic'' component of the linear variation., uuencoded gzip compressed postscript file containing 14 pages, accepted for publication in MNRAS

International audience; We present a simplified proof of the Antonov-Lebovitz theorem, asserting that any spherical barotropic star having a mass density decreasing monotonically outwards and vanishing at its surface is stable to all non-radial perturbations. We also develop a simple argument showing in a straightforward way a related but somewhat weaker result, according to which any such star is stable if and only if it is stable to radial perturbations. Extension of these results to a star with non-decreasing specific entropy distribution is also briefly discussed.

We present a global approach of non-dissipative physics. Based on symplectic mechanics this technique allows us to obtain the solution of a very large class of problems in terms of a Taylor expand. We apply this method to the problem of gravitational instability and we obtain a general expression of the gravitational potential, solution of the Vlasov- Poisson gravitational potential, solution of the Vlasov-Poisson system, as a function of time in the context of Newtonian dust cosmology., Comment: uuencoded compressed postscript file containing 14 pages, accepted for publication in ApJ

The Wirst part of the thesis focuses on the relativistic, two-body problem in the context of general relativity. More precisely, we derive a variational identity known as the ``First Law of Mechanics" that relates physical parameters of a binary system of compact objects, such as its total energy and angular momentum, to the characteristics of the objects themselves, such as their masses and spins. Our derivation is based on the gravitational skeleton formalism for compact objects at quadrupolar order, combined with an extended version of a general variational identity established for spacetimes endowed with a helical isometry describing circular orbits. We also propose a review of the various multipolar skeleton models and the different types of First Laws that exist in the literature, and discuss applications and physical implications of our results in the context of gravitational wave astronomy. The second part of the thesis deals with a classical problem of potential theory, in Newtonian gravity. In particular, we continue the exploration of isochrone potentials, introduced in the Wifties by Michel Hénon. These potentials are deWined by the property that any test particle orbits within it with a radial period that is independent of its angular momentum. After a complete classiWication of the isochrone potentials using nothing but euclidean geometry, we explore the dynamics in these potentials by classifying their orbits, providing analytical solutions to the equation of motion. Using a Hamiltonian treatment, we also derive action-angle coordinates for the isochrone problem, providing new insight of several well known result of classical celestial mechanics to all isochrone orbits, such as the Kepler equation, Bertrand's theorem and Kepler's laws of motion, and a generalization of these to all isochrone orbits. Finally, we compute the Birkhoff normal form of the corresponding Hamiltonian for a generic potential, and derive the fundamental theorem of isochrony from the inspection of the Birkhoff invariants of the system; La première partie de cette thèse se place dans le contexte du problème à deux corps en relativité générale. Nous établissons une identité variationnelle appelée ``Première Loi de la Mécanique'' qui fait le lien entre différents paramètres physiques caractérisant un système binaire d'objets compacts comme son énergie de liaison et son moment cinétique total, aux propriétés des corps, comme leur masse ou leur rotation propre. Notre résultat se base sur le modèle du ``squelette gravitationnel'' poussé à l'ordre quadrupolaire, combiné avec une généralisation d'une identité variationnelle établie pour des espaces-temps dotés d'une isométrie helicoı̈dale pour décrire des orbites circulaires. Nous présentons également un tour d'horizon des modèles de squelettes gravitationels et des différentes premières lois existant dans la littérature, et discutons des applications et de l'impact de la première loi à l'ordre quadrupolaire dans le contexte de l'astronomie gravitationnelle. La seconde partie de la thèse concerne un problème de gravitation Newtonienne, dans lequel il est question d'une classe particulière de potentiels gravitationels appelés ``potentiels isochrones''. Ceux-ci, introduits dans les années 1950 par Michel Hénon, sont déWini par la propriété que toute particule test y orbite avec une période radiale indépendante de son moment cinétique. Après avoir établi une classiWication complète de cette classe de potentiels, nous explorons la dynamique qu'ils génèrent et donnons une solution analytique des équations du mouvement exclusivement à l'aide d'outils géométriques. Puis, nous proposons une revisite du problème sous l'angle de la mécanique Hamiltonienne, permettant ainsi de voir avec un angle nouveaux certains résultats de mécanique classique, comme l'équation de Kepler, le théorème de Bertrand et les lois de Kepler, et de généraliser ceux-ci à tout orbite isochrone. EnWin, en calculant le forme normale de Birkhoff du système, nous donnons une démonstration purement mécanique du théorème fondamental de l'isochronie, basée sur l'étude des invariants de Birkhoff du système.

International audience

International audience; A survey of Michel Henon contributions to the study of globular cluster systems

The purpose of this thesis is to study the formation and properties of self-gravitating systems, insulated and uninsulated using numerical simulations of gravitational collapse of body systems. In the first part, we summarize the main analytical results concerning the system of equations coupled collisionless Boltzmann - Poisson system that models the self-gravitating collisionless, and their extension in the presence of an external field, and some analytical solutions . In a second part, we present codes that we used and we introduce the concepts of parallel and distributed computing, some elements have been parallelized using the message exchange library MPI Finally, in a final section, we present the various results of our simulations and their analysis. The first of them concerns the further study of the initial conditions needed to trigger instabilities Antonov, and the study of the internal dynamics of self-gravitating isolated systems. The second part concerns the study of these systems in orbits in an external potential, to study its influence on the formation process of self-gravitating systems by gravitational collapse.; L'objet de cette thèse est l'étude de la formation et des propriétés des systèmes auto-gravitants isolés et non isolés à l'aide de simulations numériques d'effondrements gravitationnels de systèmes à N corps. Dans une première partie, nous synthétisons les principaux résultats analytiques concernant le système d'équations couplées Boltzmann sans collisions - Poisson, qui modélise les systèmes auto-gravitants non collisionnels, et leur extension en présence d'un champ extérieur, ainsi que certaines solutions analytiques. Dans une seconde partie, nous présentons les codes que nous avons utilisés et nous introduisons des notions de calcul parallèle et réparti, certains éléments ayant été parallélisés à l'aide de la bibliothèque d'échange de messages M.P.I. Enfin, dans une dernière partie, nous exposons les différents résultats de nos simulations et leurs analyses. La première partie d'entre eux concerne l'approfondissement de l'étude des conditions initiales nécessaires au déclenchement des instabilités d'Antonov, ainsi que l'étude de la dynamique interne des systèmes auto-gravitants isolés. La seconde partie concerne l'étude de ces systèmes mis en orbites dans un potentiel extérieur, visant à étudier son influence sur le processus de formation des systèmes auto-gravitants par effondrement gravitationnels.

We study the formation of self-gravitating systems and their properties by means of N-body simulations of gravitational collapse.First, we summarize the major analytical results concerning the collisionless Boltzmann equation and the Poisson's equation which describe the dynamics of collisionless gravitational systems. We present a study of some analytical solutions of this coupled system of equations.We then present the software used to perform the simulations. Some of this has been parallelized and implemented with the aid of MPI. For this reason we give a brief overview of it.Finally, we present the results of the numerical simulations. Analysis of these results allows us to explain some features of self-gravitating systems and the initial conditions needed to trigger the Antonov instability and the radial orbit instability., Nous étudions la formation et les propriétés des systèmes auto-gravitants à l'aide de simulations numériques à N corps d'effondrements gravitationnels.Nous effectuons dans un premier temps une synthèse des principaux résultats analytiques concernant les équations de Boltzmann sans collisions et de Poisson, qui modélisent les systèmes gravitationnels non collisionnels ainsi que certaines solutions analytiques de ce système couplé d'équations.Nous présentons ensuite les codes de calcul utilisés pour les simulations. Nous avons parallélisé certains de ces codes, nous introduisons donc le calcul parallèle et la bibliothèque d'échange de message MPI.Nous exposons enfin les résultats de nos simulations, et leurs analyses. Nous déduisons de ces analyses divers résultats pouvant expliquer différentes caractéristiques des systèmes auto-gravitants ainsi que les conditions initiales nécessaires au déclenchement des instabilités d'Antonov et d'orbites radiales.