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Topological dynamics of the Weil–Petersson geodesic flow
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Pollicott, Mark, Weiss, Howard and Wolpert, Scott A.. (2010) Topological dynamics of the Weil–Petersson geodesic flow. Advances in Mathematics, Vol.223 (No.4). pp. 1225-1235. ISSN 0001-8708
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Official URL: http://dx.doi.org/10.1016/j.aim.2009.09.011
Abstract
We prove topological transitivity for the Weil–Petersson geodesic flow for real two-dimensional moduli spaces of hyperbolic structures. Our proof follows a new approach that combines the density of singular unit tangent vectors, the geometry of cusps and convexity properties of negative curvature. We also show that the Weil–Petersson geodesic flow has: horseshoes, invariant sets with positive topological entropy, and that there are infinitely many hyperbolic closed geodesics, whose number grows exponentially in length. Furthermore, we note that the volume entropy is infinite.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Advances in Mathematics |
| Publisher: | Academic Press |
| ISSN: | 0001-8708 |
| Date: | 1 March 2010 |
| Volume: | Vol.223 |
| Number: | No.4 |
| Page Range: | pp. 1225-1235 |
| Identification Number: | 10.1016/j.aim.2009.09.011 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/43863 |
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