相关论文: The dynamics of general Bianchi IX model near the …

We analyze the dynamics of a class of cosmological solutions of the Einstein-Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively…

We make comparison of the dynamics of the diagonal and nondiagonal Bianchi IX models in the evolution towards the cosmological singularity. Apart from the original variables, we use the Hubble normalized ones commonly applied in the…

Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this…

We consider some aspects of the global evolution problem of Hamiltonian homogeneous, anisotropic cosmologies derived from a purely quadratic action functional of the scalar curvature. We show that models can isotropize in the positive…

We show that the complex dynamics of the general Bianchi IX universe in the vicinity of the spacelike singularity can be approximated by a simplified system of equations. Our analysis is mainly based on numerical simulations. The properties…

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…

In this work we study the dynamics of the axisymmetric Bianchi IX cosmological model with a term of quantum potential added. As it is well known this class of Bianchi IX models are homogeneous and anisotropic with two scale factors, $A(t)$…

We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the…

The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for…

We analyze the global dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter. The matter model is not specified explicitly but only through a set of mild and physically motivated assumptions; thereby our…

We study the global dynamical behavior of spatially homogeneous solutions of the Einstein equations in Bianchi type I symmetry, where we use non-tilted elastic matter as an anisotropic matter model that naturally generalizes perfect fluids.…

The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian…

In this work the late-time evolution of Bianchi type $VIII$ models is discussed. These cosmological models exhibit a chaotic behaviour towards the initial singularity and our investigations show that towards the future, far from the initial…

An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…

We present the analyses of the asymptotic evolution of the general Bianchi IX spacetime using Hamiltonian formulation. The dynamics reveals the existence of special structures, which we call wiggles, in the physical phase space. The wiggles…

The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states…

We study the dynamics of the vacuum Bianchi IX model with timelike singularity and compare it with the dynamics of the Bianchi IX model with cosmological singularity. We show that differences in the signs of some terms in the set of…

To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on…

Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The…

We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in…