地点：行健楼学术活动室665
邀请人：周效尧副教授
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.