Winning games for bounded geodesics in moduli spaces of quadratic differentials
Jonathan Chaika Yitwah Cheung Howard Masur
We prove that the set of bounded geodesics in Teichmüller 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 Teichmüller disk and for intervals exchanges with any fixed irreducible permutation.
keywords: Schmidt games bounded trajectories. saddle connections
There exists an interval exchange with a non-ergodic generic measure
Jon Chaika Howard Masur
We prove that there exists an interval exchange transformation and a point so that the orbit of the point equidistributes according to a non-ergodic measure. That is, it is possible for a non-ergodic measure to arise from the Krylov-Bogolyubov construction of invariant measures for an interval exchange transformation.
keywords: generic points Interval exchanges Rauzy induction.

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