Schmidt games and Markov partitions

Details Schmidt games and Markov partitions Schmidt games and Markov partitions

2008-07-14

arxiv.org/abs/0807.2184v1

Mathematics

Dynamical Systems

32 pages

Scientific paper

10.1088/0951-7715/22/3/001

Let T be a C^2-expanding self-map of a compact, connected, smooth, Riemannian manifold M. We correct a minor gap in the proof of a theorem from the literature: the set of points whose forward orbits are nondense has full Hausdorff dimension. Our correction allows us to strengthen the theorem. Combining the correction with Schmidt games, we generalize the theorem in dimension one: given a point x in M, the set of points whose forward orbit closures miss x is a winning set.

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