Chaos in the mixmaster universe

Details Chaos in the mixmaster universe Chaos in the mixmaster universe

Jan 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983phrvl..50..134c&link_type=abstract

Physical Review Letters, vol. 50, Jan. 10, 1983, p. 134-137.

Mathematics

Logic

117

Astronomical Models, Chaos, Cosmology, Evolution (Development), Relativity, Universe, Einstein Equations, Nonlinear Equations, Space-Time Functions

Scientific paper

A four-dimensional system of nonlinear difference equations describing the evolution of the general relativistic "mixmaster" cosmological model is studied. The evolution splits into two parts: one given by a (chaotic) generalized Baker's transformation and the other by a (systematic) change of scales. The chaotic degrees of freedom are studied in detail. Their evolution may be described by a two-sided shift and the invariant measure for these variables is found. Strong ergodic properties (mixing, nonzero entropy) are deduced.

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