Quas, A;
Soo, T;
(2012)
Weak mixing suspension flows over shifts of finite type are universal.
Journal of Modern Dynamics
, 6
(4)
pp. 427-449.
10.3934/jmd.2012.6.427.
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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.
| Type: | Article |
|---|---|
| Title: | Weak mixing suspension flows over shifts of finite type are universal |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3934/jmd.2012.6.427 |
| Publisher version: | https://doi.org/10.3934/jmd.2012.6.427 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | square root problem, weak topological mixing., Embedding, suspension flow, universality, geodesic flow |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10089088 |
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