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

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

2010-04-26

arxiv.org/abs/1004.4401v2

Mathematics

Geometric Topology

39 Pages, 3 figures. Minor revisions

Scientific paper

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.

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