Badly approximable directions on flat surfaces and bounded geodesics in Teichmueller space

Badly approximable directions on flat surfaces and bounded geodesics in Teichmueller space

-
Jon Chaika, University of Chicago
Fine Hall 601

In this talk we show that directions on flat surfaces which are poorly approximated by saddle connection directions are a winning set for Schmidt's game. This extends a result of Schmidt for the torus and strengthens a result of Kleinbock and Weiss. It is equivalent to saying that the Teichmueller geodesic flow is bounded. We go on to show that the set of bounded geodesics is winning as a subset of projective measured laminations, answering a question of McMullen. This is joint work with Yitwah Cheung and Howard Masur.