Topological dynamics of the Weil-Petersson geodesic flow

Mark Pollicott, Howard Weiss, Scott A. Wolpert

Research output: Contribution to journalArticle

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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.

Original languageEnglish (US)
Pages (from-to)1225-1235
Number of pages11
JournalAdvances in Mathematics
Volume223
Issue number4
DOIs
Publication statusPublished - Mar 1 2010

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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