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Weak mixing suspension flows over shifts of finite type are universal
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Quas, Anthony and Soo, Terry (2012) Weak mixing suspension flows over shifts of finite type are universal. .
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Official URL: http://arxiv.org/abs/1110.1113
Abstract
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 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.
| Item Type: | Scholarly Text | ||||
|---|---|---|---|---|---|
| Alternative Title: | Anthony Quas, Terry Soo | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Publisher: | |||||
| Official Date: | August 2012 | ||||
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| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Funder: | NSERC |
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