Chaos in the Mixmaster Universe

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.