arXiv subjects

Spiros Cotsakis

Publications and source records attributed to Spiros Cotsakis.

78 records · Page 5Linked to original sources

arXiv2000

Algebraic integrability of FRW-scalar cosmologies

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 in general relativity and string theory with a variety of matter terms, by a performance of the Painlevé analysis in an effort to examine whether or not there exists a Laurent expansion of the solution about a movable pole which contains the number of arbitrary constants necessary for a general solution.

gr-qc↗

arXiv2000

Symmetries of homogeneous cosmologies

We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-interaction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi-scalar field equations become subsets of the second Bianchi jet bundle, $J^2$, and every Bianchi cosmology is naturally extended to live on a variety of $J^2$. We are interested in the existence and behaviour of extensions of arbitrary Bianchi-Lie and variational vector fields acting on the Bianchi variety and accordingly we classify all such vector fields corresponding to both Bianchi classes $A$ and $B$. We give examples of functions defined on Bianchi jet bundles which are constant along some Bianchi models (first integrals) and use these to find particular solutions in the Bianchi total space. We discuss how our approach could be used to shed new light to questions like isotropization and the nature of singularities of homogeneous cosmologies by examining the behaviour of the variational vector fields and also give rise to interesting questions about the `evolution' and nature of the cosmological symmetries themselves.

gr-qc↗

arXiv2000

Symmetry, Singularities and Integrability in Complex Dynamics IV: Painleve Integrability of Isotropic Cosmologies

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 Painlevé test is sufficient to demonstrate integrability or nonintegrability in the sense of Painlevé. For others of these models it is necessary to use a less algorithmic procedure.

gr-qc↗

arXiv2000

Ever-expanding, Isotropizing, Quadratic Cosmologies

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 asymptotic direction and that quadratic diagonal Bianchi IX models do not recollapse and may be regular initially. Although the global existence and isotropization results we prove hold quite generally, they are applied to specific Bianchi models in an attempt to describe how certain dynamical properties uncommon to the general relativity case, become generic features of these quadratic universes. The question of integrability of the models is also considered. Our results point to the fact that the more general models are not integrable in the sense of Painlevé and for the Bianchi IX case this may be connected to the validity of a BKL oscillatory picture on approach to the singularity in sharp contrast with other higher order gravity theories that contain an Einstein term and show a monotonic evolution towards the initial singularity.

gr-qc↗

arXiv2000

Symmetry, singularities and integrability in complex dynamics II: Rescaling and time-translation in two-dimensional systems

The explicit integrability of second order ordinary differential equations invariant under time-translation and rescaling is investigated. Quadratic systems generated from the linearisable version of this class of equations are analysed to determine therelationship between the Painlevé and singularity properties of the different systems. The transformation contains a parameter and for critical values, intimately related to the possession of the Painlevé Property in the parent second order equation, one finds a difference from the generic behaviour. This study is a prelude to a full discussion of the class of transformations which preserve the Painlevé Property in the construction of quadratic systems from scalar nonlinear odes invariant under time translation and rescaling.

nlin.SI↗

arXiv2000

Symmetry, singularities and integrability in complex dynamics I: the reduction problem

Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlevé property as the number of equations in each `integrable system' increases. Certain intermediate systems are constructed and also tested for the Painlevé property. The Lie symmetries are also computed for completeness.

nlin.SI↗