Journal of Nonlinear Mathematical Physics

Volume 9, Issue 1, February 2002, Pages 1 - 10

Kovalevski Exponents and Integrability Properties in Class A Homogeneous Cosmological Models

Authors
Marek Szydłowski, Marek Biesiada
Corresponding Author
Marek Szydłowski
Received 13 March 2001, Revised 10 August 2001, Accepted 17 August 2001, Available Online 1 February 2002.
DOI
https://doi.org/10.2991/jnmp.2002.9.1.1How to use a DOI?
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 VII0 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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 1
Pages
1 - 10
Publication Date
2002/02
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.1.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Marek Szydłowski
AU  - Marek Biesiada
PY  - 2002
DA  - 2002/02
TI  - Kovalevski Exponents and Integrability Properties in Class A Homogeneous Cosmological Models
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 10
VL  - 9
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.1.1
DO  - https://doi.org/10.2991/jnmp.2002.9.1.1
ID  - Szydłowski2002
ER  -