报告题目: Schmidt games and Non-dense orbits of partially hyperbolic diffeomorphisms

报告人:  Weisheng Wu(吴伟胜), China Agricultural University

时间：8月29日（星期三）下午4：00--5：00

地点：管研楼1308教室

摘要 : For a dynamical system with an ergodic measure with full support, the set of points with non-dense orbits (called non-dense set) has zero measure. However, for many systems the non-dense set has full Hausdorff dimension, and sometimes it is even a winning set for Schmidt games, which is much stronger than having full Hausdorff dimension. For example, the non-dense set of a toral endomorphism is shown to be winning and some applications to Diophantine approximation is obtained by Broderick-Fishman-Kleinbock. We show that the non-dense set of any partially hyperbolic diffeomorphism has full Hausdorff dimension and is winning for modified Schmidt games along unstable manifolds. We also discuss some further generalizations and problems.

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