Kovalevski exponents and integrability properties in class A homogeneous cosmological models

Details Kovalevski exponents and integrability properties in class A homogeneous cosmological models Kovalevski exponents and integrability properties in class A homogeneous cosmological models

2002-10-18

arxiv.org/abs/gr-qc/0210062v1

J.Nonlin.Math.Phys. 9 (2002) 1-10

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

arxiv version is already official

Scientific paper

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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