Topological dynamics of the Weil–Petersson geodesic flow
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 0001-8708Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.aim.2009.09.011
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|
|Date:||1 March 2010|
|Page Range:||pp. 1225-1235|
|Access rights to Published version:||Restricted or Subscription Access|
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