Schmidt games and markov partitions

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Some features of the site may not work correctly. DOI: 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 x0 M, the set of points whose forward orbit closures miss x0 is a winning set.

Finally, our key lemma, the… Expand. View PDF on arXiv. Save to Library Save. Create Alert Alert. Share This Paper. Methods Citations. Results Citations. Citation Type. Has PDF. Publication Type. More Filters. The topological entropy of non-dense orbits and generalized Schmidt games.

Ergodic Theory and Dynamical Systems. View 1 excerpt. The set of badly approximable vectors is strongly C1 incompressible. Mathematical Proceedings of the Cambridge Philosophical Society. Abstract We prove that the countable intersection of C1-diffeomorphic images of certain Diophantine sets has full Hausdorff dimension.

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