`a`
Journal of Modern Dynamics (JMD)
 

Weak mixing suspension flows over shifts of finite type are universal

Pages: 427 - 449, Issue 4, October 2012      doi:10.3934/jmd.2012.6.427

 
       Abstract        References        Full Text (547.7K)       Related Articles       

Anthony Quas - Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, B.C., V8W 3R4, Canada (email)
Terry Soo - Department of Mathematics and Statistics, University of Victoria, PO BOX 3060 STN CSC, Victoria, BC V8W 3R4, Canada (email)

Abstract: Let $S$ be an ergodic measure-preserving automorphism on a nonatomic 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 Hölder ceiling function. We show that if the measure-theoretic entropy of $S$ is strictly less than the topological entropy of $T$, then there exists an embedding of 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 [5] and Ratner [31], we also obtain an embedding of 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.

Keywords:  Embedding, universality, suspension flow, geodesic flow, square root problem, weak topological mixing.
Mathematics Subject Classification:  Primary: 37A35; Secondary: 37D40.

Received: October 2011;      Revised: July 2012;      Available Online: January 2013.

 References