Asymptotics of Weil-Petersson geodesics II: bounded geometry and unbounded entropy

2010/04/26 by Jeffrey Brock, Brock, Jeffrey, Howard Masur +3 · 1 citation
Mathematics · #30F60 #37D40 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1004.4401

openalex publication_date 2010/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We use ending laminations for Weil-Petersson geodesics to establish that bounded geometry is equivalent to bounded combinatorics for Weil-Petersson geodesic segments, rays, and lines. Further, a more general notion of non-annular bounded combinatorics, which allows arbitrarily large Dehn-twisting, corresponds to an equivalent condition for Weil-Petersson geodesics. As an application, we show the Weil-Petersson geodesic flow has compact invariant subsets with arbitrarily large topological entropy.

Citations

• Train tracks and the Gromov boundary of the complex of curves

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• Bounded Pluriharmonic Functions and Holomorphic Functions on Teichmüller Space II -- Poisson integral formula --

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