Journal of Modern Dynamics (JMD)

Winning games for bounded geodesics in moduli spaces of quadratic differentials

Pages: 395 - 427, Issue 3, September 2013      doi:10.3934/jmd.2013.7.395

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Jonathan Chaika - Mathematics Department, 155 S 1400 E Room 233, University of Utah, Salt Lake City, UT 84112-0090, United States (email)
Yitwah Cheung - Mathematics Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, United States (email)
Howard Masur - Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Il 60637, United States (email)

Abstract: We prove that the set of bounded geodesics in Teichm├╝ller space is a winning set for Schmidt's game. This is a notion of largeness in a metric space that can apply to measure $0$ and meager sets. We prove analogous closely related results on any Riemann surface, in any stratum of quadratic differentials, on any Teichm├╝ller disk and for intervals exchanges with any fixed irreducible permutation.

Keywords:  Schmidt games, saddle connections, bounded trajectories.
Mathematics Subject Classification:  Primary: 30F30; Secondary: 32G15.

Received: December 2012;      Available Online: December 2013.