Kovalevski exponents and integrability properties in class A homogeneous cosmological models

Abstract

Qualitative approach to homogeneous anisotropic Bianchi class A models in terms of dynamical systems reveals a hierarchy of invariant manifolds. By calculating the Kovalevski Exponents according to Adler - van Moerbecke method we discuss how algebraic integrability property is distributed in this class of models. In particular we find that algebraic nonintegrability of vacuum Bianchi VII_0 model is inherited by more general Bianchi VIII and Bianchi IX vacuum types. Matter terms (cosmological constant, dust and radiation) in the Einstein equations typically generate irrational or complex Kovalevski exponents in class A homogeneous models thus introducing an element of nonintegrability even though the respective vacuum models are integrable.

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References in corpus (1)

• The mixmaster universe: A chaotic Farey tale

Cited by in corpus (5)

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• Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario
• Analytic integrability of the Bianchi Class A cosmological models with 0<= k<1
• Integrability of anisotropic and homogeneous Universes in scalar-tensor theory of gravitation