Symmetry, Singularities and Integrability in Complex Dynamics IV Painleve Integrability of.pdf

SYMMETRY, SINGULARITIES AND INTEGRABILITY IN COMPLEX DYNAMICS IV: ´ PAINLEVE INTEGRABILITY OF ISOTROPIC COSMOLOGIES 1 2,3 4 J. Miritzis , P.G.L. Leach and S. Cotsakis GEODYSYC, Department of Mathematics, University of the Aegean, Karlovassi 83 200, Greece We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory 0 with a variety of matter terms. For some of these models the standard Painlev´e test is sufficient to demonstrate 0 integrability or nonintegrability in the sense of Painlev´e. For others of these models it is necessary to use a less 0 algorithmic procedure. 2 v 1. Introduction [8, 9] have pointed the way to a rigorous application o of the singularity analysis. N In the modelling of various phenomena in relativistic In this paper, which is the fourth in a series [19, 20, 6 cosmology the final result of the modelling process is a 21] devoted to the investigation of connections between system of ordinary differential equations, whose solu- the three main topics in dynamics namely, symmetry, 1 tion is by no means obvious. Generally these systems singularities and integrability, the topics which super- v are of the first order and autonomous, so that, if the ficially are unrelated in their mathematics and yet are 9 system is two-dimensional, one is assured of the exis- intimately intertwined, we apply the techniques of sin- 1 tence of solu