English

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

Geometric Topology 2010-05-28 v2

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.

Keywords

Cite

@article{arxiv.1004.4401,
  title  = {Asymptotics of Weil-Petersson geodesics II: bounded geometry and unbounded entropy},
  author = {Jeffrey Brock and Howard Masur and Yair Minsky},
  journal= {arXiv preprint arXiv:1004.4401},
  year   = {2010}
}

Comments

39 Pages, 3 figures. Minor revisions