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

Jeffrey Brock, Howard Masur, Yair Minsky

Published 2010-04-26, updated 2010-05-27Version 2

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.