Speaker：Dr. Weisheng Wu

                       China Agricultural University

Title:  On nondense orbits and entropy of partially hyperbolic diffeomorphisms

       Time：12 June 2019, 16:00

Location：实验楼105

Abstract:  Partially hyperbolic diffeomorphisms of smooth manifolds are important topics in differentiable dynamical systems and smooth ergodic theory. Such systems have high complexity, possessing an abundance of nondense orbits from topological viewpoint, as well as various invariant measures from ergodic viewpoint. On one hand, we show that the set of points with nondense orbit has full Hausdorff dimension, and in fact it enjoys a much stronger property, that is, winning for Schmidt games. On the other hand, we study the Kolmogorov-Sinai entropy for invariant measures of partially hyperbolic diffeomorphisms. We introduce new notions of unstable entropy and pressure, and establish a variational principle relating unstable metric entropy and unstable topological entropy. We also prove Katok’s intermediate entropy conjecture for partially hyperbolic homogenous systems, which says that there are various ergodic measures whose entropies attain any number between zero and the topological entropy of the system.

Speaker Introduction：吴伟胜现为中国农业大学应用数学系副教授，2014年博士毕业于美国宾夕法尼亚州立大学，2014-2016北京大学博士后。研究方向为动力系统与遍历论。先后主持中国博士后科学基金特别资助项目和国家自然科学基金青年基金，多篇文章发表在“Adv. Math.”,“Trans. Amer. Math. Soc.”，“Ergodic Theory Dynam. Systems”等学术期刊上。