Ergodic theory of the mixmaster universe in higher space-time dimensions. II

Details Ergodic theory of the mixmaster universe in higher space-time dimensions. II Ergodic theory of the mixmaster universe in higher space-time dimensions. II

Sep 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987jsp....48.1269e&link_type=abstract

Journal of Statistical Physics, Volume 48, Issue 5-6, pp. 1269-1282

Mathematics

Logic

12

Mixmaster Model, Ergodic Theory, Chaos, Einstein Equations, Cosmological Singularity, Kaluza-Klein Cosmology

Scientific paper

The topological dynamics of the mixmaster models in space-time dimension d+1 are investigated. We use a new parametrization to reduce the mixmaster map to a translation combined with an appropriate isometry or a dilating inversion. For d⩽9, we show that the mixmaster map is ergodic and topologically mixing. For d⩾10, the mixmaster map reduces to the identity after a finite number of iterations, except for a set of initial data with zero Lebesgue measure.

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