The order of chaos on a Bianchi-IX cosmological model

Details The order of chaos on a Bianchi-IX cosmological model The order of chaos on a Bianchi-IX cosmological model

Dec 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986gregr..18.1263b&link_type=abstract

General Relativity and Gravitation (ISSN 0001-7701), vol. 18, Dec. 1986, p. 1263-1274.

Mathematics

6

Chaos, Cosmology, Astronomical Models, Einstein Equations, Iteration, Maps, Oscillations, Singularity (Mathematics)

Scientific paper

The purpose of this paper is to analyze the chaotic behavior that can arise on a type IX cosmological model using methods from dynamic-systems theory and symbolic dynamics. Specifically, instead of the Belinski-Khalatnikov-Lifschitz model, the iterates of a monotonously increasing map of the circle with a discontinuity are employed. For the Hamiltonian dynamics of Misner's (1969) Mixmaster model, the iterates of a noninvertible map are introduced. An equivalence between these two models can easily be brought about by translating them in symbolic-dynamical terms. The resulting symbolic orbits can be inserted in an ordered tree structure set, and so an effective counting and classification of all period orbits can be presented.

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