天元讲堂（1.4-1.5）张金华报告
报告题目：Partial entropy, empirical measures and u-entropy formula (part 1)
报告人 张金华（巴黎南大学）
报告时间 2018年1月4日09:30-10:30
报告地点 维格堂319
报告摘要 In this talk, we will recall the notions of measurable partition, the entropy of measurable partition and so on defined by Rokhlin. We will also recall the properties of entropy of measurable partition.
报告题目：Partial entropy, empirical measures and u-entropy formula (part 2)
报告人 张金华（巴黎南大学）
报告时间 2018年1月4日10:30-11:30
报告地点 维格堂319
报告摘要 The partial entropy along unstable foliation was given by Ledrappier-Young to measure the relation between the entropy, Lyapunov exponent and dimension. We will recall the definition of partial entropy and some known results on this direction.
报告题目：Partial entropy, empirical measures and u-entropy formula (part 3)
报告人 张金华（巴黎南大学）
报告时间 2018年1月4日11:30-12:30
报告地点 维格堂319
报告摘要 We will show that in C^1-setting, for a partially hyperbolic attracting set with the splitting of the form E^{cs}/oplus E^{u}, each empirical measure of typical points in the attracting basin of the attracting set satisfies u-entropy formula. With this, we get many interesting corollaries. For instance, when it is restricted in C^1+/alpha-setting, such empirical measure is a Gibbs u-state. This is a joint work with S.Crovisier and D. Yang.
报告人 张金华（巴黎南大学）
报告时间 2018年1月4日09:30-10:30
报告地点 维格堂319
报告摘要 In this talk, we will recall the notions of measurable partition, the entropy of measurable partition and so on defined by Rokhlin. We will also recall the properties of entropy of measurable partition.
报告题目：Partial entropy, empirical measures and u-entropy formula (part 2)
报告人 张金华（巴黎南大学）
报告时间 2018年1月4日10:30-11:30
报告地点 维格堂319
报告摘要 The partial entropy along unstable foliation was given by Ledrappier-Young to measure the relation between the entropy, Lyapunov exponent and dimension. We will recall the definition of partial entropy and some known results on this direction.
报告题目：Partial entropy, empirical measures and u-entropy formula (part 3)
报告人 张金华（巴黎南大学）
报告时间 2018年1月4日11:30-12:30
报告地点 维格堂319
报告摘要 We will show that in C^1-setting, for a partially hyperbolic attracting set with the splitting of the form E^{cs}/oplus E^{u}, each empirical measure of typical points in the attracting basin of the attracting set satisfies u-entropy formula. With this, we get many interesting corollaries. For instance, when it is restricted in C^1+/alpha-setting, such empirical measure is a Gibbs u-state. This is a joint work with S.Crovisier and D. Yang.
报告题目：Non-hyperbolic ergodic measures approached by horseshoes (part 1)
报告人 张金华（巴黎南大学）
报告时间 2018年1月5日09:30-10:30
报告地点 维格堂319
报告摘要 In this talk, we will consider a certain open class of partially hyperbolic diffeomorphisms and we will show that each non-hyperbolic ergodic measure is approached by hyperbolic periodic measures in weak* topology. This is a joint work with C. Bonatti.
报告题目：Non-hyperbolic ergodic measures approached by horseshoes (part 2)
报告人 张金华（巴黎南大学）
报告时间 2018年1月5日10:30-11:30
报告地点 维格堂319
报告摘要 For the precise open set of partially hyperbolic diffeomorphisms we discussed in the previous talk, we will show that each non-hyperbolic ergodic measure with positive entropy is approached by hyperbolic horseshoes in weak*-topology and in entropy. This is a joint work with D. Yang.
报告人 张金华（巴黎南大学）
报告时间 2018年1月5日09:30-10:30
报告地点 维格堂319
报告摘要 In this talk, we will consider a certain open class of partially hyperbolic diffeomorphisms and we will show that each non-hyperbolic ergodic measure is approached by hyperbolic periodic measures in weak* topology. This is a joint work with C. Bonatti.
报告题目：Non-hyperbolic ergodic measures approached by horseshoes (part 2)
报告人 张金华（巴黎南大学）
报告时间 2018年1月5日10:30-11:30
报告地点 维格堂319
报告摘要 For the precise open set of partially hyperbolic diffeomorphisms we discussed in the previous talk, we will show that each non-hyperbolic ergodic measure with positive entropy is approached by hyperbolic horseshoes in weak*-topology and in entropy. This is a joint work with D. Yang.