相关论文: The Bianchi Ix (MIXMASTER) Cosmological Model is N…

The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the…

We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory with a variety of matter terms. For some of these models the standard Painlev\'{e} test is sufficient to demonstrate…

It has recently been argued that there might exist a four-parameter analytic solution to the Bianchi IX cosmological model, which would extend the three-parameter solution of Belinskii et al. to one more arbitrary constant. We perform the…

The mixmaster model has always been a field of controversy in the literature regarding its (non)integrability. In this work, we make use of a generalized definition of a class of nonlocal conserved charges in phase space to demonstrate that…

The Bianchi IX cosmological model in vacuum can be represented by several six-dimensional dynamical systems. In one of them we present a new closed form solution expressed by a third Painleve' function.

We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case…

There exist many situations where an ordinary differential equation admits a movable critical singularity which the test of Kowalevski and Gambier fails to detect. Some possible reasons are: existence of negative Fuchs indices, insufficient…

We investigate the integrability of cosmic strings in Bianchi III space-time in presence of a bulk viscous fluid by applying a new technique. The behaviour of the model is reduced to the solution of a single second order nonlinear…

We consider a five dimensional vacuum cosmology with Bianchi type-IX spatial geometry and an extra non-compact coordinate. Finding a new class of solutions, we examine and rule out the possibility of deterministic chaos. We interpret this…

For dynamical systems of dimension three or more the question of integrability or nonintegrability is extended by the possibility of chaotic behaviour in the general solution. We determine the integrability of isotropic cosmological models…

We investigate the integrability of an anisotropic universe with matter and cosmological constant formulated as Bianchi IX models. The presence of the cosmological constant causes the existence of a critical point in the finite part of the…

We remind the way to obtain integrable models with non-minimally coupled scalar fields. We are interesting to models with bounce solutions and compare bounce solutions in two known integrable models. We show that only one model has a bounce…

The second order Ordinary Differential Equation which describes the unknown part of the solution space of some vacuum Bianchi Cosmologies is completely integrated for Type III, thus obtaining the general solution to Einstein's Field…

The question of the integrability of the mixmaster model of the Universe, presented as a dynamical system with finite degrees of freedom, is investigated in present paper. As far as the model belongs to the class of pseudo-Euclidean…

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive…

Motivated by the structure of one-loop vacuum polarization effects in curved spacetime we discuss a non-minimal extension of the Einstein-Maxwell equations. This formalism is applied to Bianchi I models with magnetic field. We obtain…

We consider the conformal Einstein equations for polytropic perfect fluid cosmologies which admit an isotropic singularity. For the polytropic index gamma strictly greater than 1 and less than or equal to 2 it is shown that the Cauchy…

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…

In this work, we are investigating the problem of integrability of Bianchi class A cosmological models. This class of systems is reduced to the form of Hamiltonian systems with exponential potential forms. The dynamics of Bianchi class A…

We examine whether the Painlev\'e property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we…