Weak mixing suspension flows over shifts of finite type are universal

Details Weak mixing suspension flows over shifts of finite type are universal Weak mixing suspension flows over shifts of finite type are universal

2011-10-05

arxiv.org/abs/1110.1113v1

Mathematics

Dynamical Systems

24 pages, 1 figure

Scientific paper

Let S be an ergodic measure-preserving automorphism on a non-atomic probability space, and let T be the time-one map of a topologically weak mixing suspension flow over an irreducible subshift of finite type under a Holder ceiling function. We show that if the measure-theoretic entropy of the S is strictly less than the topological entropy of T, then there exists an embedding from the measure-preserving automorphism into the suspension flow. As a corollary of this result and the symbolic dynamics for geodesic flows on compact surfaces of negative curvature developed by Bowen and Ratner, we also obtain an embedding from the measure-preserving automorphism into a geodesic flow, whenever the measure-theoretic entropy of S is strictly less than the topological entropy of the time-one map of the geodesic flow.

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