Volume 9, Issue 1, February 2002, Pages 1 - 10
Kovalevski Exponents and Integrability Properties in Class A Homogeneous Cosmological Models
Marek Szydłowski, Marek Biesiada
Received 13 March 2001, Revised 10 August 2001, Accepted 17 August 2001, Available Online 1 February 2002.
- https://doi.org/10.2991/jnmp.2002.9.1.1How to use a DOI?
- 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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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 -