Non-integrability of the mixmaster universe

Year: 1995

Authors: Christiansen F., Rugh HH., Rugh SE.

Autors Affiliation: Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy;
Inst. Hautes Etud. Sci., 35 Route de Chartres, Bures-sur Yvette, France;
Univ. Copenhagen, Niels Bohr Inst., Blegdamsvej 17, Copenhagen, Denmark)

Abstract: We comment on an analysis by Contopoulos et al which demonstrates that the governing six-dimensional Einstein equations for the mixmaster spacetime metric pass the ARS or reduced Painleve test. We note that this is the case irrespective of the value, I, of the generating Hamiltonian which is a constant of motion. For I < 0 we find numerous closed orbits with two unstable eigenvalues strongly indicating that two additional first integrals apart from the Hamiltonian cannot exist and thus that the system, at least for this case, is very probably not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. Journal/Review: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL

Volume: 28 (3)      Pages from: 657  to: 667

KeyWords: chaotic behavior; cosmology; systems
DOI: 10.1088/0305-4470/28/3/019

Citations: 16
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