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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. doi:10.1016/j.aim.2009.09.011 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Advances in Mathematics | ||||
Publisher: | Academic Press | ||||
ISSN: | 0001-8708 | ||||
Official Date: | 1 March 2010 | ||||
Dates: |
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Volume: | Vol.223 | ||||
Number: | No.4 | ||||
Page Range: | pp. 1225-1235 | ||||
DOI: | 10.1016/j.aim.2009.09.011 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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