Symmetry, singularities and intregrability in complex dynamics VII: Integrability Properties of FRW-Scalar Cosmologies

TL;DR

This paper investigates the integrability of cosmological dynamical systems in FRW-scalar cosmologies using the Painlevé criterion, comparing it with dynamical systems analysis to evaluate its effectiveness.

Contribution

It provides a comparative analysis of Painlevé integrability and dynamical systems methods in the context of FRW-scalar cosmologies, highlighting their relative advantages.

Findings

Painlevé analysis offers insights into system integrability.

Comparison reveals strengths and limitations of each method.

Results inform the applicability of Painlevé in covariant systems.

Abstract

This paper considers some physically interesting cosmological dynamical systems in the FRW-scalarfield category which are examined for integrability according to the criterion of Painlev\'e. In the literature these systems have been examined from the point of view of dynamical systems and the results from the two disparate methods of analysis are compared. This allows some more general comments to be made on the use of the Painlev\'e method in covariant systems.