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Integrability and Explicit Solutions in Some Bianchi Cosmological Dynamical Systems
Abstract:Abstract

The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G 2 cosmologies. By using Darboux’s theory in order to study ordinary differential equations in the complex projective plane ??2 we solve the Bianchi V models totally. Moreover, we carry out a study of Bianchi VI models and first integrals are given in particular cases.
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