Journal of Statistical Physics, Vol. 48, Nos. 5/6, 1987. p. 1269-1282.
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.