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A new map of the sky representing the degree of randomness in the cosmic microwave background (CMB) temperature has been obtained. The map based on estimation of the Kolmogorov stochasticity parameter clearly distinguishes the contribution of the Galactic disk from the CMB and reveals regions of various degrees of randomness that can reflect the properties of inhomogeneities in the Universe. For example, among the high randomness regions is the southern non-Gaussian anomaly, the Cold Spot, with a stratification expected for the voids. Existence of its counterpart, a Northern Cold Spot with almost identical randomness properties among other low-temperature regions is revealed. By its informative power, Kolmogorov's map can be complementary to the CMB temperature and polarization sky maps., Comment: A & A (in press), to match the published version, 4 pages, 5 figs, 2 Tables

The Kolmogorov stochasticity parameter (KSP) is applied to quantify the degree of randomness (stochasticity) in the temperature maps of the Cosmic Microwave Background radiation maps. It is shown that, the KSP for the WMAP5 maps is about twice higher than that of the simulated maps for the concordance \LambdaCDM cosmological model, implying the existence of a randomizing effect not taken into account in the model. As was revealed recently, underdense regions in the large scale matter distributions, i.e the voids, possess hyperbolic and hence randomizing properties. The degree of randomness for the Cold Spot appears to be about twice higher than the average over the mean temperature level spots in the sky, which supports the void nature of the Cold Spot. Kolmogorov's parameter then acts as a quantitative tracer of the voids via CMB., Comment: A&A Lett (in press), 2 pages, 1 Table

We continue investigation of the hidden plane-mirror symmetry in the distribution of excursion sets in cosmic microwave background (CMB) temperature anisotropy maps, previously noticed in the three-year data of the Wilkinson microwave anisotropy probe (WMAP), using the WMAP 5 years maps. The symmetry is shown to have higher significance, \chi^2 < 1.7, for low multipoles \ell < 5, while disappearing at larger multipoles, \chi^2 > 3.5 for \ell > 10. The study of the sum and difference maps of temperature inhomogeneity regions, along with simulated maps, confirms its existence.The properties of these mirroring symmetries are compatible with those produced by the Sachs-Wolfe effect in the presence of an anomalously large component of horizon-size density perturbations, independent of one of the spatial coordinates, and/or a slab-like spatial topology of the Universe., Comment: A&A accepted

The degree of randomness in the cosmic microwave background (CMB) maps has been shown to be measurable and indicative of the hyperbolic effect of voids on the propagation of the photon beams. In terms of an introduced porosity parameter, we now obtain the criterion for a hyperbolicity due to domination of voids in the line-of-sight direction. The criterion seems to be supported by the parameters of 30 Mpc scale voids revealed by the galactic redshift surveys. The importance of the geometrical effect of the voids is also due to their possible role in the temperature independent ellipticity of the excursion sets, as well as in the nature of dark energy. The role of possible larger scale inhomogeneities, from superclusters to semi-Hubble scale, in this effect remains yet unclear., Comment: A&A Lett (in press), 3 pages, no figures

The properties of geodesics flow are studied in a Friedmann-Robertson-Walker metric perturbed due to the inhomogeneities of matter. The basic, averaged Jacobi equation is derived, which reveals that the low density regions (voids) are able to induce hyperbolicity, even if the global curvature of the Universe is zero or slightly positive. It is shown that the energy independence is a characteristic property of these geometric effects. The importance of these conclusions is determined by the temperature independent ellipticity of excursion sets and regions of different randomness found in Kolmogorov CMB maps., Comment: Europhys.Lett., in press

We study inhomogeneities in the distribution of the excursion sets in the Cosmic Microwave Background (CMB) temperature maps obtained by the three years survey of the Wilkinson Microwave Anisotropy Probe (WMAP). At temperature thresholds |T|<90 \mu K, the distributions of the excursion sets with over 200 pixels are concentrated in two regions, nearly at the antipodes, with galactic coordinates l= 94^\circ.7, b= 34^\circ.4 and l= 279^\circ.8, b= -29^\circ.2. The centers of these two regions drift towards the equator when the temperature threshold is increased. The centers are located close to one of the vectors of \ell =3 multipole. The two patterns of the substructures in the distribution of the excursion sets are mirrored, with \chi^2=0.7-1.5. There is no obvious origin of this effect in the noise structure of WMAP, and there is no evidence for a dependence on the galactic cut. Would this effect be cosmological, it could be an indication of an anomalously large component of horizon-size density perturbations, independent of one of the spatial coordinates, and/or of a non-trivial slab-like spatial topology of the Universe.

Chaotic dynamics essentially defines the global properties of gravitating systems, including, probably, the basics of morphology of galaxies. We use the Ricci curvature criterion to study the degree of relative chaos (exponential instability) in core-halo gravitating configurations. We show the existence of a critical core radius when the system is least chaotic, while systems with both smaller and larger core radius will typically possess stronger chaotic properties., Comment: In proceedings of MG11 meeting, Berlin 2006

The measurement of the Compton edge of the scattered electrons in GRAAL facility in European Synchrotron Radiation Facility (ESRF) in Grenoble with respect to the Cosmic Microwave Background dipole reveals up to 10 sigma variations larger than the statistical errors. We now show that the variations are not due to the frequency variations of the accelerator. The nature of Compton edge variations remains unclear, thus outlining the imperative of dedicated studies of light speed anisotropy.

We describe briefly a novel interpretation of the physical nature of dark energy (DE), based on the vacuum fluctuations model by Gurzadyan & Xue, and describe an internally consistent solution for the behavor of DE as a function of redshift. A key choice is the nature of the upper bound used for the computation of energy density contributions by vacuum modes. We show that use of the comoving horizon radius produces a viable model, whereas use of the proper horizon radius is inconsistent with the observations. After introduction of a single phenomenological parameter, the model is consistent with all of the curently available data, and fits them as well as the standard cosmological constant model, while making testable predictions. While some substantial interpretative uncertainties remain, future developments of this model may lead to significant new insights into the physical nature of DE., Comment: To appear in Proc. UCLA Conference "Dark Matter 2006", eds. D. Cline et al., Nuclear Pysics B, in press (2006); 5 pages

Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data confirm the ellipticity of anisotropies of Cosmic Microwave Background (CMB) maps, found previously for Boomerang and WMAP 1-year high sensitivity maps. The low noise level of the WMAP latter data enable also to show that, the ellipticity is a property not described by the conventional cosmological model fitting the power spectrum of CMB. As a large scale anomaly, the ellipticity characteristics are consistent with the effect of geodesics mixing occurring in hyperbolic Universe. Its relation to other large scale effects, i.e. to suppressed low multipoles, as well as to dark energy if the latter is due to vacuum fluctuations, is then an arising issue., Comment: to appear in Phys. Lett. A

The formula for the dark energy, derived by Padmanabhan in a recent Letter to Editor (Class.Quantum Grav. September 2005, the formula given in its Abstract), was actually derived 4 years earlier ourselves in astro-ph/0105245; Mod.Phys.Lett. A18, 561, 2003. Among dozens of references in that Letter, no quotation to our paper. Based on the same Zeldovich idea on vacuum fluctuations, Padmanabhan derives it from scaling considerations, while we had gone into more details and shown that the formula fits the observed value of the cosmological constant if l=0 modes are relevant., Comment: missing factor 2 added; refs added

Bit strings rather than byte files can be a mode of transmission both for intelligent signals and for travels of extraterrestrial life. Kolmogorov complexity, i.e. the minimal length of a binary coded string completely defining a system, can then, due to its universality, become a key concept in the strategy of the search of extraterrestrials. Evaluating, for illustration, the Kolmogorov complexity of the human genome, one comes to an unexpected conclusion that a low complexity compressed string - analog of Noah's ark - will enable the recovery of the totality of terrestrial life. The recognition of bit strings of various complexity up to incompressible Martin-L\"{o}f random sequences, will require a different strategy for the analysis of the cosmic signals. The Fermi paradox "Where is Everybody?" can be viewed under in the light of such information panspermia, i.e. a Universe full of traveling life streams., Comment: Refs added. To appear in The Observatory

The ellipticity of the anisotropy spots of the Cosmic Microwave Background measured by the Wilkinson Microwave Anisotropy Probe (WMAP) has been studied. We find an average ellipticity of about 2, confirming with a far larger statistics similar results found first for the COBE-DMR CMB maps, and then for the BOOMERanG CMB maps. There are no preferred directions for the obliquity of the anisotropy spots. The average ellipticity is independent of temperature threshold and is present on scales both smaller and larger than the horizon at the last scattering. The measured ellipticity characteristics are consistent with being the effect of geodesics mixing occurring in an hyperbolic Universe, and can mark the emergence of CMB ellipticity as a new observable constant describing the Universe. There is no way of simulating this effect. Therefore we cannot exclude that the observed behavior of the measured ellipticity can result from a trivial topology in the popular flat $\Lambda$-CDM model, or from a non-trivial topology., Comment: 10 pages, 5 figures, the version to appear in Mod.Phys.Lett. A

We have studied the angular fluctuations in the speed of light with respect to the apex of the dipole of Cosmic Microwave Background (CMB) radiation using the experimental data obtained with GRAAL facility, located at the European Synchrotron Radiation Facility (ESRF) in Grenoble. The measurements were based on the stability of the Compton edge of laser photons scattered on the 6 GeV monochromatic electron beam. The results enable to obtain a conservative constraint on the anisotropy in the light speed variations \Delta c(\theta)/c < 3 10^{-12}, i.e. with higher precision than from previous experiments., Comment: The published version: reported at the workshop "Testing the Equivalence Principle in Space and on Ground" (STEP), Pescara, Italy, September, 2004

Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the substructure of clusters of galaxies, instability in Wheeler-DeWitt superspace. The choice of the problems aimed to show also the diversity of approaches and mathematical tools, which include the geometric criterion (Ricci) of relative instability in many dimensional systems, the estimation of Kolmogorov-Sinai entropy, the hyperbolicity in pseudo-Riemannian spaces, etc., Comment: Lectures at the Xth Brazilian School of Cosmology and Gravitation, July-August, Rio de Janeiro, 2002

A theoretical attempt to identify the physical process responsible for the afterglow emission of Gamma-Ray Bursts (GRBs) is presented, leading to the occurrence of thermal emission in the comoving frame of the shock wave giving rise to the bursts. The determination of the luminosities and spectra involves integration over an infinite number of Planckian spectra, weighted by appropriate relativistic transformations, each one corresponding to a different viewing angle in the past light cone of the observer. The relativistic transformations have been computed using the equations of motion of GRBs within our theory, giving special attention to the determination of the equitemporal surfaces. The only free parameter of the present theory is the ``effective emitting area'' in the shock wave front. A self consistent model for the observed hard-to-soft transition in GRBs is also presented. When applied to GRB 991216 a precise fit $(\chi^2\simeq 1.078)$ of the observed luminosity in the 2--10 keV band is obtained. Similarly, detailed estimates of the observed luminosity in the 50--300 keV and in the 10--50 keV bands are obtained., Comment: 10 pages, 4 figures, to appear on Int.J.Mod.Phys.D

The recent study of BOOMERanG 150 GHz Cosmic Microwave Background (CMB) radiation maps have detected ellipticity of the temperature anisotropy spots independent on the temperature threshold. The effect has been found for spots up to several degrees in size, where the biases of the ellipticity estimator and of the noise are small. To check the effect, now we have studied, with the same algorithm and in the same sky region, the WMAP maps. We find ellipticity of the same average value also in WMAP maps, despite of the different sensitivity of the two experiments to low multipoles. Large spot elongations had been detected also for the COBE-DMR maps. If this effect is due to geodesic mixing and hence due to non precisely zero curvature of the hyperbolic Universe, it can be linked to the origin of WMAP low multipoles anomaly., Comment: More explanations and two references added

We discuss the algorithmic information approach to the analysis of the observational data on the Universe. Kolmogorov complexity is proposed as a descriptor of the Cosmic Microwave Background (CMB) radiation maps. An algorithm of computation of the complexity is described, applied, first, to toy models and then, to the data of the Boomerang experiment. The sky maps obtained via the summing of two independent Boomerang channels reveal threshold independent behavior of the mean ellipticity of the anisotropies, thus indicating correlations present in the sky signal and possibly carrying crucial information on the curvature and the non-Friedmannian, i.e. accelerated expansion of the Universe. Similar effect has been detected for COBE-DMR 4 year maps. Finally, as another application of these concepts, we consider the possible link between the CMB properties, curvature of the Universe and arrows of time., Comment: Talk at XXII Solvay Conference on Physics "The Physics of Communication" (Delphi, November 24-29, 2001); the discussion included

We have measured the ellipticity of several degree scale anisotropies in the BOOMERanG maps of the Cosmic Microwave Background (CMB) at 150 GHz. The average ellipticity is around 2.6-2.7. The biases of the estimator of the ellipticity and for the noise are small in this case. Large spot elongation had been detected also for COBE-DMR maps. If this effect is due to geodesic mixing, it would indicate a non precisely zero curvature of the Universe which is among the discussed reasons of the WMAP low multipole anomaly. Both effects are related to the diameter of the Universe: the geodesics mixing through hyperbolic geometry, low multipoles through boundary conditions.This common reason can also be related with the origin of the the cosmological constant: the modes of vacuum fluctuations conditioned by the boundary conditions lead to a value of the cosmological constant being in remarkable agreement with the supernovae observations., Comment: Added: two co-authors and a comment on the possible relation of the discussed CMB properties with the origin of the observed value of the cosmological constant

I argue that the widely adopted framework of stellar dynamics survived since 1940s, is not fitting the current knowledge on non-linear systems. Borrowed from plasma physics when several fundamental features of perturbed non-linear systems were unknown, that framework ignores the difference in the role of perturbations in two different classes of systems, in plasma with Debye screening and gravitating systems with no screening. Now, when the revolutionary role of chaotic effects is revealed even in planetary dynamics i.e. for nearly integrable systems, one would expect that for stellar systems, i.e. non-integrable systems, their role have to be far more crucial. Indeed, ergodic theory tools already enabled to prove that spherical stellar systems are exponentially instable due to N-body interactions, while the two-body encounters, contrary to existing belief, are not the dominating mechanism of their relaxation. Chaotic effects distinguish morphological and other properties of galaxies. Using the Ricci curvature criterion, one can also show that a central massive object (nucleus) makes the N-body gravitating system more instable (chaotic), while systems with double nuclei are even more instable than those with a single one., Comment: Talk delivered at Joint Discussion 11, IAU XXVth General Assembly, Sydney, July,2003, to appear in Highlights of Astronomy, vol.13

The graph-theoretical S-tree technique developed for the study of the nonlinear N-body systems, is used for the study for the first time of the substructure of a high redshift cluster of galaxies, namely of MS 1054-03, z\simeq 0.8. Nearby galaxy clusters studied via the same S-tree code reveal several clearly distinguished subgroups with significant bulk velocities. Therefore the study of distant clusters can enable to trace the evolution of their dynamics over cosmological time scales. The study of the MS 1054-03 showed a different structure, i.e. no evidence of merging subgroups but only of a core of galaxies with velocity dispersion about 700 km s^{-1} while the velocity dispersion of the main cluster 1870 km s^{-1}. Further study of samples of high redshift clusters will enable to conclude whether this discrepancy in the structure and dynamics between nearby and distant galaxy clusters is a genuine evolutionary effect., Comment: to appear in NUovo Cimento B

We advance a new viewpoint on the connection between the the thermodynamical and cosmological arrows of time, which can be traced via the properties of Cosmic Microwave Background (CMB) radiation. We show that in the Friedmann-Robertson-Walker Universe with negative curvature there is a necessary ingredient for the existence of the thermodynamical arrow of time. It is based on the dynamical instability of motion along null geodesics in a hyperbolic space. Together with special (de-correlated) initial conditions, this mechanism is sufficient for the thermodynamical arrow, whereas the special initial conditions alone are able to generate only a pre-arrow of time. Since the negatively curved space will expand forever, this provides a direct connection between the thermodynamical and cosmological arrows of time. The structural stability of the geodesic flows on hyperbolic spaces and hence the robustness of the proposed mechanism is especially stressed. We then point out that the main relations of equilibrium statistical thermodynamics (including the second law) do not necessarily depend on any arrow of time. Finally we formulate a {\it curvature anthropic principle}, which stipulates the negative curvature as a necessary condition for the time asymmetric Universe with an observer. CMB has to carry the signature of this principle as well.

The major problem posed by the Fermi-Pasta-Ulam work was the relaxation (thermalization) of a many-body system. We review two approaches to this problem, the ergodic theory and Langevin (stochastic) equation ones, which have been applied for the description of statistical mechanics of stellar systems. Among the particular problems that we consider, are 1-dimensional long-range interacting systems and iterated maps and 3-dimensional N-body gravitating systems., Comment: To appear in "Fermi and Astrophysics" (Proceed. of ICRA Workshop dedicated to 100th birthday of E.Fermi, Rome-Pescara, 2001), World Scientific. New version in WS macros

The properties of the Cosmic Microwave Background (CMB) maps carry valuable cosmological information. Here we report the results of the analysis hot and cold CMB anisotropy spots in the BOOMERanG 150 GHz map in terms of number, area, ellipticity, vs. temperature threshold. We carried out this analysis for the map obtained by summing independent measurement channels (signal plus noise map) and for a comparison map (noise only map) obtained by differencing the same channels. The anisotropy areas (spots) have been identified for both maps for various temperature thresholds and a catalog of the spots has been produced. The orientation (obliquity) of the spots is random for both maps. We computed the mean elongation of spots obtained from the maps at a given temperature threshold using a simple estimator. We found that for the sum map there is a region of temperature thresholds where the average elongation is not dependent on the threshold. Its value is ~ 2.3 for cold areas and ~ 2.2 for hot areas. This is a non-trivial result. The bias of the estimator is less than 0.4 for areas of size less than 30', and smaller for larger areas. The presence of noise also biases the ellipticity by less than 0.3. These biases have not been subtracted in the results quoted above. The threshold independent and random obliquity behaviour in the sum map is stable against pointing reconstruction accuracy and noise level of the data, thus confirming that these are actual properties of the dataset. The data used here give a hint of high ellipticity for the largest spots. Analogous elongation properties of CMB anisotropies had been detected for COBE-DMR 4-year data. If this is due to geodesics mixing, it would point to a non zero curvature of the Universe., Comment: Addendums on the more detailed description of the algorithms and on the non zero curvature

We describe a method for recovering of the substructure, internal dynamics and geometrical shapes of clusters of galaxies. Applying the method to the Virgo cluster, we, first, reveal the substructure of the central 4 arc degree field of the Virgo cluster by means of S-tree technique. The existence of three main subgroups of galaxies is revealed and their dynamical characteristics are estimated. Then, using the previously suggested technique (Gurzadyan and Rauzy 1997), the bulk flow velocities of the subgroups are evaluated based on the distribution of the redshifts of the galaxies. The results enable us also to obtain a secure indication of the elongation of the Virgo cluster and its positional inclination., Comment: to appear in Int.Journ.Mod.Phys.D

We advance the viewpoint that only relevant modes of the vacuum fluctuations, namely, with wavelengths conditioned by the size, homogeneity, geometry and topology of the Universe, do contribute into the cosmological constant. A formula is derived which relates the cosmological constant with the size of the Universe and the three fundamental constants: the velocity of light, Planck and Newton gravitational constants. Then the current value of the cosmological constant remarkably agrees with the value indicated by distant supernovae observations, i.e. is of the order of the critical density. Thus the cosmological constant had to be smaller than the matter density in the past and will be bigger in the future., Comment: the version to appear in Mod.Phys.Lett. A

The mean redshift of the core of the Coma cluster - cz = 6953 km s^{-1} and its dispersion \sigma=949 km s^{-1} are obtained by means of the analysis of the substructures of this cluster by using the S-tree method. The existence of three subgroups of galaxies is revealed, one of them is associated with the cD galaxy NGC 4874, the other -- with NGC 4889. It is argued that these subgroups are {\it galaxy associations}, i.e. galactic dynamical entities moving within the main cluster. Thus we conclude that the non-stationarity of the dynamical processes ongoing in the Coma core is due to the merging of small-scale galaxy associations, rather than of two equal sized clusters. We provide the lists of the galaxies of the associations, the observational study of which can be of particular interest., Comment: to appear in New Astronomy

Some points related to the exponential instability of N-body gravitating systems and which are misinterpreted in various papers are clarified. Exponential instability is a phenomenon essentially responsible for the relaxation, evolutionary, morphological and other properties of certain type of galaxies and star clusters., Comment: in "The Chaotic Universe", (V.G.Gurzadyan and R.Ruffini, eds.), p.245, World Sci. 2000; the paper by M.Valluri and D.Merritt in the same volume, p.229; astro-ph/9909403

The properties of the Cosmic Microwave Background (CMB) radiation must be different in flat, positively and negatively curved universes. This fact leads to a direct way of determining the geometry of the universe. The signature of the predicted effect of geodesic mixing, i.e., of the `chaotic' behavior of photon beams in negatively curved spaces peculiar to Anosov systems with strong statistical properties, has been detected while studying the COBE-DMR 4-year data \cite{GT}. This possible observation of the negative curvature of the universe suggests the need to search for more effective ways to analyze the CMB data expected from forthcoming high precision experiments. Information theory offers such a descriptor for the CMB sky maps - the Kolmogorov complexity - as well as provides novel insight into the problem of the loss of information and time asymmetry in a hyperbolic universe., Comment: to appear in: V.G.Gurzadyan and R.Ruffini (Eds.) "The Chaotic Universe", World Sci

We consider the problem of numerical computation of the Kolmogorov complexity and the fractal dimension of the anisotropy spots of Cosmic Microwave Background (CMB) radiation. Namely, we describe an algorithm of estimation of the complexity of spots given by certain pixel configuration on a grid and represent the results of computations for a series of structures of different complexity. Thus, we demonstrate the calculability of such an abstract descriptor as the Kolmogorov complexity for CMB digitized maps. The correlation of complexity of the anisotropy spots with their fractal dimension is revealed as well. This technique can be especially important while analyzing the data of the forthcoming space experiments., Comment: LATEX, 3 figures

The relation between the thermodynamical and cosmological arrows of time is usually viewed in the context of the initial conditions of the Universe. It is a necessary but not sufficient condition for ensuring the thermodynamical arrow. We point out that in the Friedmann-Robertson-Walker Universe with negative curvature, k=-1, there is the second necessary ingredient. It is based on the geodesic mixing - the dynamical instability of motion along null geodesics in hyperbolic space. Kolmogorov (algorithmic) complexity as a universal and experimentally measurable concept can be very useful in description of this chaotic behavior using the data on Cosmic Microwave Background radiation. The formulated {\it curvature anthropic principle} states the negative curvature as a necessary condition for the time asymmetric Universe with an observer., Comment: Revtex, to appear in the proceedings of the workshop THE CHAOTIC UNIVERSE, Eds.V.G.Gurzadyan, R.Ruffini, World Sci

The information theory approach is suggested to the Cosmic Microwave Background (CMB) problem for negatively curved homogeneous and isotropic Universe. Namely, the Kolmogorov complexity of anisotropy of spots in CMB sky maps is proposed as a new descriptor for revealing crucial cosmological information, particularly on the curvature of the Universe. Such profound descriptor can be especially valuable while analyzing the data of forthcoming space and ground based experiments MAP, Planck surveyor, CAT, etc., Comment: to appear in Europhysics Letters

The problem of the relative motion of the substructures of the Local Group of galaxies revealed via S-tree method, as well as of the velocity of the Local Group itself, is considered. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via 3D reconstruction procedure, which uses the information on the radial velocities of the galaxies, but not on their distances. Once the bulk motion of substructures is estimated, in combination with the observed CMB dipole we also consider the mean velocity of the Local Group itself. Assigning the Local Group the mean motion of its main substructures we evaluate its peculiar velocity in Milky Way frame V(LG->MW)= (-7 \pm 303,-15 \pm 155 ,+177 \pm 144) or 178 km/s toward galactic coordinates l=245 and b=+85. Combined with CMB dipole V(MW->CMB), we obtain Local Group velocity in CMB frame: V(LG->CMB) = (-41\pm 303,-497\pm 155,445 \pm 144) or 668 km/s towards l=265 and b=42. This estimation is in good agreement, within 1 sigma level, with the estimation of Yahil et al (1977)., Comment: To be published in MNRAS

The results of an analysis of the substructure of 1 degree field galaxies of the Virgo cluster by means of the S-tree technique developed by Gurzadyan et al, are represented. The existence of 3 main subgroups is shown and their dynamical parameters are obtained. The mass centers of the subgroups appear to be aligned in the direction parallel to the elongation of the Virgo cluster. The morphological analysis shows some domination of dwarf galaxies in the subgroup A containing M 87, and existence of two spiral galaxies N4425 and N4461; the latter fact can be crucial for the estimation of the distance of the Virgo cluster by means of the search of Cepheids in that spirals., Comment: Latex 14 pages, 2 figures; to appear in Astrofizika

The geodesics followed by cosmic microwave background (CMB) photons show different behaviours depending on the geometry of space. Namely, the effect of `mixing geodesics' predicts a distinct signature in CMB maps: threshold-independent elongated anisotropy spots in negatively curved geometries. We have found statistically significant sign for spot elongation in the COBE four year maps. This can be a direct indication for the negative curvature of the Universe., Comment: Talk given at VIII Marcel Grossmann Meeting (Jerusalem, 1997); to appear in proceedings; Latex 4 pages

The S-tree method is used to estimate the redshift of the core of Coma cluster - $cz = 6953$ km s$^{-1}$ and dispersion $\sigma=949$ km s$^{-1}$. The existence of three subgroups of galaxies is revealed, one of them is associated with the cD galaxy NGC 4874, another - with NGC 4889. It is argued that these subgroups are 'galaxy associations', i.e. galactic dynamical entities moving through the main cluster. The non-stationarity of the dynamical processes ongoing in the Coma core is concluded., Comment: to appear in the proceedings of Coma Cluster meeting (Marseille, June, 1997)

The results of the analysis of the subclustering in a sample of ESO Nearby Abell Cluster Survey (ENACS) galaxy clusters, with data complemented from other studies, are presented. The analysis is performed by using the S-tree method enabling one to study the hierarchical properties of clusters, namely by the detection of the main physical cluster and of its subgroups. The results indicate: (a) systematically lower genuine cluster velocity dispersions than known from previous studies; (b) existence of 2-3 subgroups in each cluster. Due to certain properties of specific dynamical entities, we denote these subgroups as galaxy associations, which can become an essential challenge for formation mechanisms of galaxy clusters., Comment: To appear in M.N.R.A.S., Latex 25 pages,10 Figures (Fig.1.1-1.10)

The problem of reconstruction of the 3D velocities of clusters of galaxies from the redshift distribution of galaxies of the cluster is formulated. Though numerical simulations show the impossibility of direct use of Ambartsumian's formula derived for the stellar systems because of the small number of objects in the clusters, an additional physical assumption on the form of the searched velocity distribution can lead to the possibility of obtaining the transverse velocity of the cluster. The accuracy of the proposed reconstruction procedure is estimated., Comment: to appear in Astrofizika, vol.40, 1997; LaTex, 4 pages, 1 figure, *.ps figure can be obtained from the authors

The existence of period-doubling bifurcations is shown for the Konishi-Kaneko map. The value of the control parameter $k_{\infty}$ corresponding to the transition to the chaotic phase is estimated, along with the Feigenbaum universal number. This type of facts can be crucial in diagnosis of chaos in stellar dynamics., Comment: Latex file 4 pages; Il Nuovo Cimento, vol.112B, 1997

When considering the statistical properties of a bundle of cosmic microwave background (CMB) photons propagating through space, the effect of `mixing geodesics' appears with a distinct signature that depends on the geometry of space. In a Universe with negative curvature this effect is expected to produce elongated anisotropy spots on CMB maps. We used COBE-DMR data to look for such effect. Based on the analysis of a measure of eccentricity of hot spots it appears that there is a clear indication of an excess eccentricity of hot spots with respect to that expected from noise alone. This result must be interpreted with caution as this effect can be due in part to galactic emission. If the detected eccentricity of anisotropy spots can be attributed to the effect of mixing it implies the negative curvature of the Universe and a value of $\Omega < 1$., Comment: Text 5 pages, AA Latex style file, with 2 postscript figures. To appear in Astronomy and Astrophysics

Results of precise measurements of the periods of pulsars discovered in the central regions of globular clusters are shown to be approaching the capabilities of testing the existence of a central black hole. For example, in the case of M 15 the available data on two pulsars PSR 2129+1210A and PSR 2129+1209D seem to exclude the existence of a black hole, the presence of which was instead supported by recent Hubble Space Telescope data on surface brightness profile (Yanny et al. 1994). The fluctuations of the gravitational field caused by the stars of the system are enough to explain the acceleration observed for both pulsars. In the case of the Galactic center, additional data are needed for similar definite conclusions., Comment: laa-style Latex 4 pages; to appear in Astronomy and Astrophysics

We report the results of an analysis of the hierarchical properties of the cluster of galaxies Abell 119. Observational data from the ESO Nearby Abell Cluster Survey (ENACS) are used, complemented by data from previous studies, while the analysis is performed with the S-tree method. The main physical system and its three subgroups with truncated Gaussian velocity distributions are identified; due to their remarkable physical features and possible cosmogonical mission we call these subgroups ``galaxy associations''. The mass centre of the core of main system is shown to coincide with the X-ray centre of the cluster. An alignment of the mass centres of the 3 galaxy associations is also shown., Comment: Latex file, 7 pages, 2 figures, .ps files can be obtained from the authors. To appear in The Observatory, vol.116, No.1134, 1996

As was shown before (Gurzadyan and Kocharyan, 1992, 1993ab) the statistical properties (exponential mixing) of motion of CMB photon beams in Friedmann Universe with negative curvature can have definite observable consequences including the decrease of the CMB anisotropy amplitude after the last scattering, distortion of images on CMB sky maps. Here we consider one more consequence concerning the behaviour of temperature autocorrelation function C(\theta,\beta), where \theta is the modulation (separation) angle, and \beta the observing beam effective angle. We prove that in the Universe with negative curvature any spectrum of perturbations at last scattering epoch becomes a scale-invariant by present time. It is also predicted that the temperature autocorrelation function should increase while obtained from measurements with small beam sizes within some mixing beam angle., Comment: 6 pages, plain LaTeX, IC/93/419