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We investigated the smoothing of the cosmic background radiation (CBR) through gravitational scatterings. The CBR is gravitationally scattered by galaxies, clusters of galaxies, and superclusters during the travel from the last scattering surface. Although the effect of the gravitational scatterings was thought to be unimportant, we found that the scatterings by superclusters reduce the anisotropy by a large factor. This result is explained by the fact that the distance between two light rays increases exponentially through multiple scatterings. This exponential growth occurs if the distance is smaller than the critical distance determined by the number density of the scattering objects. We found that the gravitational scatterings by superclusters can reduce the temperature anisotropy of the CBR at present time by a large factor, in angular scales up to a few degrees. [ABSTRACT FROM AUTHOR]

We investigated the evolution of clusters of galaxies using direct N-body simulations in which each galaxy is modeled by many particles. We found that the galaxies in the inner region of cluster lose their mass more rapidly than do those in the outer region. Therefore the galaxies in the inner region become smaller than those in the outer region. Significant fraction of the total mass of the cluster escapes from galaxies into the intracluster space. They form diffuse halo around the center of cluster. We also found that the mass (m) and the velocity dispersion (σ) satisfy the relation, m ∝ σ4. This tendency is consistent with the Faber-Jackson relation, which L ∝ σ4. This implies that the Faber-Jackson relation is result of the evolution of the galaxies driven by interactions with other galaxies and the tidal field of the parent cluster. [ABSTRACT FROM AUTHOR]

Spherical stellar systems offer what is probably the best example of regular stellar systems and, accordingly, quite a few models are available for them with distribution functions depending on energy alone or on both energy and angular momentum. Real stellar systems, however, are subject to several effects that, although ignored when deriving those models, can cause irregular orbits to appear in them. Among those effects, the interaction of stellar systems is an extreme example of phenomena that, except for a few general analytical results, can only be investigated through numerical methods. While recognizedly a difficult subject, the study of interacting spherical stellar systems offers an interesting and almost virgin field to chaos researchers. We summarize here the investigations of other authors and our own, with a detailed discussion of the different physical processes relevant to this problem, and with particular emphasis on the most recent results. [ABSTRACT FROM AUTHOR]

High-softening two-dimensional models, frequently employed in N-body experiments, do not provide faithful simulations of real galactic discs. A prescription (♠) is given for choosing meaningful values of the softening length. In addition, a local stability criterion (♣) is given for choosing meaningful input values of the Toomre parameter for a given softening length. Such a criterion should also provide a key to a correct interpretation of computational results in terms of real phenomena. [ABSTRACT FROM AUTHOR]

Quasi-linear theory is applied to the wave-star interaction of a differentially-rotating stellardisk of a galaxy. Under the influence of growing spiral waves the velocity dispersion of stars increases, and the resulting distortion in phase space leads to a decrease in the growth rate of the waves, and the Jeans instability ends. Due to interactions of stars with unstable waves the relaxation of the stellar disk of the Galaxy occurs in ≈ 109 years. The theory is confirmed by N-body computer simulations. [ABSTRACT FROM AUTHOR]

We prove the existence of a unique global minimum energy state for a self-gravitating system whose mass and a "quasi-entropy" assume a priori given values. [ABSTRACT FROM AUTHOR]

During the recent years, a lot of papers have dealt with the triggering and growth of chaotic orbital behaviour in dynamical models of galaxies. A question remains still open: Which is the tolerable percentage of chaotic orbits in self-gravitating equilibrium models describing the various morphologies of observed galaxies? Selected results will be presented as a step towards the understanding of this question. They concern triaxial systems such as barred and elliptical galaxies. [ABSTRACT FROM AUTHOR]

The collisionless limit of the N-body problem is often justified by the long 2-body relaxation time. Several other possibilities exist by which stellar systems can evolve and relax faster than previously expected. In particular observations and numerical experiments suggest that fractal distribution functions can spontaneously occur. The understanding of the complex evolution of N-body systems such as galaxies requires presently complementary paradigms. [ABSTRACT FROM AUTHOR]

The ergodic properties of a one-dimensional gravitational system belonging to the microcanonical ensemble are studied. This system, constituted of equal-mass particles, exhibits very strong binary structures which prevent the system to be ergodic and then to reach the theoretical curves predicted by Rybicki. The presence of the binary structure (called molecule is examined through two criterions. The first one is given by a topological property based on the order relation of the one-dimensional systems; the second one is the internal energy of the molecule. At last the study of the molecule stability indicates that it strongly depends on initial conditions. [ABSTRACT FROM AUTHOR]

We present a new approach to deal with the problem of stability of collisionless stellar systems. This technique, based on the symplectic structure of the Vlasov-Poisson system, allows us to derive a new stability criterion for general systems. It is very useful in the anisotropic spherical case. [ABSTRACT FROM AUTHOR]

Numerical experiments have been performed with 340-body equal-mass systems having a central point mass. The results indicate that the exponential growth of perturbations in position is partly caused by the "graininess" of the particle distribution, but part is associated with the smooth field of the particles. [ABSTRACT FROM AUTHOR]

The problem of the study of N-body gravitating systems is considered from the point of view of the relevance of the computer-created model with the physical one. It is shown that due to the discontinuity of the Lyapunov characteristic exponents their numerical calculations cannot be a proper method of studying the instability properties of the system. This fact occurs both for systems with softened (independent on the way of softening) and, what is more interesting, even for unsoftened (i.e., pure Newtonian) potential. [ABSTRACT FROM AUTHOR]

We have investigated the effect of the numerical error of the force calculation on the accuracy of the result of collisionless N-body simulations. Our main result is that force calculation with a low accuracy — a few percent for each particle pair — is sufficient, irrespective of the number of particles. Higher accuracy is useless since the discreteness noise, i.e., the two-body relaxation effect, dominates the error. We have performed numerical experiments for two different cases: a special-purpose machine with low-precision hardware and the tree-code. In both cases, the two-body relaxation effect dominates the error and the effect of the error in the force calculation is practically negligible for all cases we tried. [ABSTRACT FROM AUTHOR]

We have shown hot to treat consistently a set of rapidly mixing particles. It is possible to devise various dissipative transformations and then correct them to conserve the mass, centers of mass and velocity, and especially the total angular momentum. Furthermore, for simple linear friction laws it is possible to specify in advance the energy dissipation. In that case the conservation of the other integrals constraints the energy loss not exceed a maximum value. Among all the possible corrective transformations that we have described above, only a small part may be applicable in actual physical systems. In real systems further constraints restrict the possible mixing and thus the dissipation rate, e.g., when a flow expands its internal viscosity is much smaller than when it contracts. Only studies with specific problems will allow us to choose the "right" way to model dissipation and mixing. At least the formulaiton here is general and consistent with the most fundamental constraints that fluids are though to follow. For example in a schock, another instance where the hydrodynamic description fails, the shock conditions require precisely to conserve mass and momentum. Here not only these quantities, but also the angular momentum are automatically conserved. Presently we are experimenting with these transformations. We have implemented the correcting transformations in simple N-body systems (N ≲ 100, and in large-scale N-body simulations (N ≈ 2 − 105). It is straightforward to check that the integrals are indeed conserved exactly. Applications to disc galaxies are investigated in which self-gravity is calculated with a Particle-Mesh method in a 3D polar grid (Pfenniger & Friedli 1991, 1993). This approach allows to simulate gas at large scale much more efficiently that traditional hydrodynamical codes, and is not less realistic with respect to the ISM that the hydrodynamical models since the ISM is highly inhomogeneous at small scale, and no global equation of state is known. In comparison with the SPH technique, 10 times more particles runs 10 times faster with the law discussed in Sect. 3.2, essentially because there is no need to find the neares neighbours. Instead all the particles within the same grid cells used for the gravitation calculation mix their momentum at a specified rate. [ABSTRACT FROM AUTHOR]

The Konishi-Kaneko system is modified to a continuous time system. The dynamical and thermodynamical stability is investigated in this paper. The dynamical stability is investigated with the use of the collisionless Boltzmann equation. The predicted growth rates agree excellently with those obtained from N-body simulations. Thermodynamic arguments show that the system has clustered equilibrium states as well as uniform states for 1/T > 4π/kn, where k is a coupling constant and n is the number density of particles. The clustered equilibrium is thermodynamically stable and the uniform state is unstable for 1/T > 4π/kn. This stability criterion is the same as that of the dynamical stability. [ABSTRACT FROM AUTHOR]

Elliptical galaxies seem to have two inconsistent characters in their dynamical structures: triaxial velocity dispersions of the stars suggest that the elliptical galaxies consist of regular stellar orbits, whereas nonlinear interaction in self-gravitating many-body systems makes the elliptical galaxies chaotic. A new type of chaos, "stable chaos", in which orbits do not change significantly although they have orbital instability (positive Lyapunov exponent), is expected to give the key to clarify the dynamical structure of elliptical galaxies. As a first step, we examine whether the stable chaos appears or not in one-dimensional self-gravitating mass sheet systems. [ABSTRACT FROM AUTHOR]

N-particle systems of 1-D globally coupled maps are numerically investigated to show the formation of spatial order in chaotic dynamics of Hamiltonian systems. The system itinerates between ordered and disordered states by its deterministic dynamics. Phase space structure and existence of long-time tail reveals that the ordered state is supported by hierarchical motion around ruins of regular orbits (KAM tori and islands. [ABSTRACT FROM AUTHOR]

The properties of the billiard vary with the energy E of the bouncing ball. These are explored through the surface of section. The billiard is almost integrable for very small or very large values of E. It looks ergodic in a range of values of E. The main families of periodic orbits are shown. [ABSTRACT FROM AUTHOR]

A concise account is given here of some recent results concerning the dynamical properties of Hamiltonian systems with many degrees of freedom. Some of the main theoretical points of this research field are also briefly discussed and compared with the outcomes of recent numerical simulations. New results, obtained with a differential geometrical approach to Hamiltonian dynamics, are also presented together with a mention of their consequences for a deeper understanding of the dynamical properties of self-gravitating N-body systems. [ABSTRACT FROM AUTHOR]

What are the main advantages of the present treatment of stellar dynamics from the point of view of theory of dynamcal systems? The first major gain seems to be the precise definitions and hence the unique meaning of the terminology and notation often used in stellar dynamics, such as relaxation, instability, chaos, etc. In particular, we have seen that the term relaxation cannot necessarily be attributed only to processes which involve exchange of energy between particles. The classical problem of the relaxation of an ideal gas is an illustration of this fact. Another example is the term chaos: only systems possessing at least the property of mixing, and not purely ergodic ones, can be called chaotic, e.g., such terms as ergodic chaos should be considered as having no meaning. Spherical stellar systems can thus be designated as chaotic systems. The second advantage is the possibility of obtaining deeper insight into the fundamental properties of N-body systems and the discovery of underlying relationships between them. The relations between the negativity of the two-dimensional curvature determined by the Newtonian interaction potential, the exponential instability of phase trajectories and relaxation driving effects for spherical stellar systems, the properties of Lie groups, and the conclusion regarding the exponential instability of flow (but not relaxation) in the consideration of disk systems, are examples of this fact. The absence of a universal relaxation time scale indicates that the attempts to estimate relaxation time scales which describe the observed states of galaxies and star clusters by using numerical simulations of 100 or 1000 or even more particle models of N-body systems with a somehow softened potential cannot make much sense. In particular, the exponential growth of errors in gravitating N-body systems as first found by Miller [20]cannot be directly related to relaxation time scales since the same effect can be seen, for example, in the integrable 2-body Kepler problem (for the discussion of N-body numerical simulations see [21,22]). The third advantage is the development of new methods and criteria which can be used both in analytical and especially in computer studies of N-body systems. Studies already completed indicate that the Ricci curvature method can be a useful tool for numerically investigating the local (in time) instability properties not only of stellar configurations, but also of plasma and other many-dimensional systems. Finally, this approach offers more unsolved problems, some of which are listed in [3], than those which are presently solvable. I think this can be considered as another advantage rather than as a weak point of this technique. [ABSTRACT FROM AUTHOR]

The stability problem in Hamiltonian dynamics is discussed in the light of Nekhoroshev's theorem. This guarantees a form of weak stability, namely referred to finite (rather than infinite) times. Applications are discussed for the restricted problem of three bodies and for the problem of energy equipartition in statistical mechanics. [ABSTRACT FROM AUTHOR]

This review describes some of the high-resolution observations of the cores of globular clusters, obtained from the ground and with the Hubble Space Telescope (HST). Contrary to galaxies, whose distances are generally larger than 1 Mpc, implying unresolved stellar distributions, globular clusters have distances of the order of 10 kpc, which allow HST to resolve the brightest stars into grainy stellar distributions. We specifically discuss here some recent results on the galactic globular clusters NGC 6397, M15, and 47 Tucanae. [ABSTRACT FROM AUTHOR]

This review discusses two intriguing problems posed by observations of early-type galaxies: First, the existence of a so-called fundamental plane of elliptical galaxies and its thickness impose strong constraints on their global dynamical structures, stellar populations, and the relation of dark to visible matter in them. Second, the prevalence of extreme core-halo structures among the nucleated dwarf galaxies. Finally, some general remarks are made about the standard density forms of galactic subsystems, including dark halos. These empirical findings provide strong constraints and valuable clues for models of galaxy formation. They may point towards the existence of preferred dynamical structures in galaxies, perhaps globally stable or maximum entropy states, reached through different formative histories. [ABSTRACT FROM AUTHOR]