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Asymptotics of Weil–Petersson Geodesics II: Bounded Geometry and Unbounded Entropy

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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 theWeil–Petersson geodesic flow has compact invariant subsets with arbitrarily large topological entropy.

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Authors and Affiliations

  1. Department of Mathematics, Brown University, Providence, RI, 02912, USA

    Jeffrey Brock

  2. Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL, 60637, USA

    Howard Masur

  3. Department of Mathematics, Yale University, New Haven, CT, 06520, USA

    Yair Minsky

Authors
  1. Jeffrey Brock
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  2. Howard Masur
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  3. Yair Minsky
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Corresponding author

Correspondence to Jeffrey Brock.

Additional information

J. Brock was partially supported by NSF Grants DMS-0906229 and DMS-0553694, and by a John Simon Guggenheim Foundation Fellowship. H. Masur was partially supported by NSF Grant DMS-0905907. Y. Minsky was partially supported by NSF Grants DMS-0504019 and DMS-0554321.

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Brock, J., Masur, H. & Minsky, Y. Asymptotics of Weil–Petersson Geodesics II: Bounded Geometry and Unbounded Entropy. Geom. Funct. Anal. 21, 820–850 (2011). https://doi.org/10.1007/s00039-011-0123-x

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  • DOI: https://doi.org/10.1007/s00039-011-0123-x

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