天元讲堂：张金华系列报告
报告题目：New examples of dynamically coherent partially hyperbolic diffeomorphisms I
报告人 张金华（北京大学）
报告时间 2017年5月19日09:00-10:00
报告地点 维格堂319
报告摘要 There was a fantastic problem: is it possible to classify partially hyperbolic diffeomorphism? In this talk, we will first talk about the classical examples of partially hyperbolic diffeomorphisms on 3-manifolds and then we overview the classifying results obtained so far.
报告题目：New examples of dynamically coherent partially hyperbolic diffeomorphisms II
报告人 张金华（北京大学）
报告时间 2017年5月19日10:00-11:00
报告地点 维格堂319
报告摘要 In a very recent work of Bonatti-Parwani-Potrie, the authors built a dynamically coherent partially hyperbolic diffeomorphism on a 3-manifold. The diffeomorphism is obtained by composing the time t-map of a special non-transitive Anosov flow with a Dehn twist along a transverse torus. This example is highly 'different' from the classical ones.
报告题目：New examples of dynamically coherent partially hyperbolic diffeomorphisms III
报告人 张金华（北京大学）
报告时间 2017年5月19日11:00-12:00
报告地点 维格堂319
报告摘要 In this talk, we will explain the novelty of new examples from last talk. Then we will show that in fact, many topological properties of the invariant foliations of classical ones are preserved by the new ones, although their dynamical behavior on the invariant foliations is very different.
报告人 张金华（北京大学）
报告时间 2017年5月19日09:00-10:00
报告地点 维格堂319
报告摘要 There was a fantastic problem: is it possible to classify partially hyperbolic diffeomorphism? In this talk, we will first talk about the classical examples of partially hyperbolic diffeomorphisms on 3-manifolds and then we overview the classifying results obtained so far.
报告题目：New examples of dynamically coherent partially hyperbolic diffeomorphisms II
报告人 张金华（北京大学）
报告时间 2017年5月19日10:00-11:00
报告地点 维格堂319
报告摘要 In a very recent work of Bonatti-Parwani-Potrie, the authors built a dynamically coherent partially hyperbolic diffeomorphism on a 3-manifold. The diffeomorphism is obtained by composing the time t-map of a special non-transitive Anosov flow with a Dehn twist along a transverse torus. This example is highly 'different' from the classical ones.
In this talk, we will show that one can start with any non-transitive Anosov flow to construct partially hyperbolic diffeomorphisms by composing the time t-map of the Anosov flow with Dehn twists along transverse tori. This is a joint work with Christian Bonatti.
报告题目：New examples of dynamically coherent partially hyperbolic diffeomorphisms III
报告人 张金华（北京大学）
报告时间 2017年5月19日11:00-12:00
报告地点 维格堂319
报告摘要 In this talk, we will explain the novelty of new examples from last talk. Then we will show that in fact, many topological properties of the invariant foliations of classical ones are preserved by the new ones, although their dynamical behavior on the invariant foliations is very different.
报告题目：On the convexity of the closure of the set of ergodic measures I
报告人 张金华（北京大学）
报告时间 2017年5月20日13:00-14:00
报告地点 维格堂319
报告摘要 We will first talk about a classical result in the hyperbolic setting stating that the periodic measures are dense among invariant measures supported on a single hyperbolic basic set, and in particular, this implies that the set of invariant measures is a Poulsen simplex. This result is due to K. Sigmund. Then we overview the results for extending Sigmund's result to the non-hyperbolic setting.
报告人 张金华（北京大学）
报告时间 2017年5月20日13:00-14:00
报告地点 维格堂319
报告摘要 We will first talk about a classical result in the hyperbolic setting stating that the periodic measures are dense among invariant measures supported on a single hyperbolic basic set, and in particular, this implies that the set of invariant measures is a Poulsen simplex. This result is due to K. Sigmund. Then we overview the results for extending Sigmund's result to the non-hyperbolic setting.
报告题目：On the convexity of the closure of the set of ergodic measures II
报告人 张金华（北京大学）
报告时间 2017年5月20日14:00-15:00
报告地点 维格堂319
报告摘要 In this talk, we will show that there always exist non-hyperbolic ergodic measures for the known C^1-robustly non-hyperbolic examples.
报告人 张金华（北京大学）
报告时间 2017年5月20日14:00-15:00
报告地点 维格堂319
报告摘要 In this talk, we will show that there always exist non-hyperbolic ergodic measures for the known C^1-robustly non-hyperbolic examples.
Such measures can be obtained as the limit of periodic measures. This gives the difficulties for extending Sigmund's result.
报告题目：On the convexity of the closure of the set of ergodic measures III
报告人 张金华（北京大学）
报告时间 2017年5月20日15:00-16:00
报告地点 维格堂319
报告摘要 In this talk, we attempt to extend Sigmund's result to partially hyperbolic setting. We will consider an open set of partially hyperbolic diffeomorphisms with robustly minimal strong foliations. We will show that the closure of the set of non-hyperbolic ergodic measures is a convex. Moreover, every non-hyperbolic ergodic measure is approached by periodic measures in weak*-topology. This is a joint work with Christian Bonatti.
报告人 张金华（北京大学）
报告时间 2017年5月20日15:00-16:00
报告地点 维格堂319
报告摘要 In this talk, we attempt to extend Sigmund's result to partially hyperbolic setting. We will consider an open set of partially hyperbolic diffeomorphisms with robustly minimal strong foliations. We will show that the closure of the set of non-hyperbolic ergodic measures is a convex. Moreover, every non-hyperbolic ergodic measure is approached by periodic measures in weak*-topology. This is a joint work with Christian Bonatti.