2018年“动力系统中的遍历理论”研讨会
会议主办单位：苏州大学动力系统与微分方程研究中心
威尼斯人-威尼斯人娱乐场
会议地点：威尼斯人-威尼斯人娱乐场
会议时间：2018年7月2日-7月5日
2018年7月2日 下午报到
1. 报告人 胡虎翼（密西根州立大学,教授）
报告时间 2018年7月3日09:00-09:50,
报告题目：转移算子简介(I)
摘要：主要介绍Ruelle定义的转移算子及其在双曲动力系统中的应用
报告地点：维格堂319
2018年7月3日09:50-10:00，茶歇
2. 报告人 胡虎翼（密西根州立大学,教授）
报告题目：转移算子简介(II)
摘要：主要介绍Ruelle定义的转移算子及其在双曲动力系统中的应用
报告时间 2018年7月3日10:00-10:50,
报告地点：维格堂319
3. 报告人 王式柔（阿尔伯塔大学，博士）
报告时间 2018年7月3日11:00-11:50,
报告题目：Synchronization in discrete-time,discrete-state Random Dynamical Systems
报告摘要：We characterize synchronization fordiscrete-time, discrete-state random dynamical systems, with random andprobabilistic Boolean networks as particular examples. By studyingmultiplicative ergodic properties of the induced linear cocycle, we show such arandom dynamical system with a finite state set synchronizes if and only if theLyapunov exponent $0$ has simple multiplicity. For the case of countable stateset, characterization of synchronization is provided in term of the spectralsubspace corresponding to the Lyapunov exponent $-/infty$. In addition, forboth cases of finite and countable state sets, the mechanism of partialsynchronization is described by partitioning the state set into synchronizedsubsets.
报告时间 2018年7月3日11:00-11:50,
报告地点：维格堂319
4. 报告人 何宝林（上海师范大学，副教授）
报告时间 2018年7月3日14:00-14:50,
报告题目：Entropy of general diffeomorphisms of line
报告摘要：We studythe continuity of toplogical entropy of general diffeomorphisms on line. First, weprove that the entropy map iscontinuous with respect to strong $C^0$-topology on the union of uniformlytopologically hyperbolic diffeomorphisms contained in $/diff_b^r (/r) /cup /diff_0^r (/r) $ ( whose first derivative is bounded or uniformlyaway from zero). It is a $C^0$-open and $C^r$-dense subset of $/diff_b^r(/r) /cup /diff_0^r (/r) $, $r=1,2,/cdots, /infty$, and $/omega$.Second, we prove that the entropy map is locally constant at several classes ofdiffeomorphisms on line, for example uniformly topologically hyperbolic orientation-perservingdiffeomorphisms. Third, we prove that entropy map is continuous on a$C^r$-generic subset of $/diff^r (/RR)$, $r /geq 1$. In the end, we show thatuniformly topologically hyperbolicity is not a sufficient condition for generaldiffeomorphisms on line.
报告地点：维格堂319
5. 报告人 崔鸿飞（中科院武汉物理数学研究所，副研究员）
报告时间 2018年7月3日15:00-15:50,
报告题目：Decay ofcorrelations for Interval Maps with Critical Points and Singularities
报告摘要：For someinterval maps with critical points or singularities (may with discontinuitiesat critical points and singularities), we prove the existence and decay ofcorrelations of an invariant probability measure which is absolutely continuouswith respect to Lebesgue measure.
报告地点：维格堂319
2018年7月3日15:50-16:00, 茶歇
6. 报告人 史逸（北京大学，博士）
报告时间 2018年7月3日16:00-16:50,
报告题目：C^r Closing Lemma for PartiallyHyperbolic Diffeomorphisms on 3-Manifolds
报告摘要：The C^r Closing Lemma is a famousopen problem in dynamical systems. Smale listed it as one of the mathematicalproblems in this century. In this talk, we will show that C^r Closing Lemmaholds for partially hyperbolic diffeomorphisms on 3-manifolds, i.e. everyno-wandering point is C^r closable. Moreover, we will also show that C^rClosing Lemma holds for conservative partially hyperbolic diffeomorphisms on3-manifolds, i.e. C^r-generic conservative partially hyperbolic diffeomorphismson 3-manifolds have dense periodic points. This is a joint work with S. Gan.
报告地点：维格堂319
2018年7月3日17:00-17:30, 讨论咨询
2018年7月4日
1. 报告人 胡虎翼（密西根州立大学，教授）
报告时间 2018年7月4日09:00-09:50,
报告题目：转移算子简介(III)
摘要：主要介绍Ruelle定义的转移算子及其在双曲动力系统中的应用
报告地点：维格堂319
2018年7月4日09:50-10:00，茶歇
2. 报告人 胡虎翼（密西根州立大学,教授）
报告时间 2018年7月4日10:00-10:50,
报告题目：转移算子简介(IV)
摘要：主要介绍Ruelle定义的转移算子及其在双曲动力系统中的应用
报告地点：维格堂319
3.报告人 糜泽亚（南京信息工程大学，博士）
报告时间 2018年7月4日11:00-11:50,
报告题目：Partially hyperbolic diffeomorphims withmostly expanding centers
报告摘要：We show the existence and finiteness of SRB(Physical) measures forpartially hyperbolic diffeomorphisms admitting mostly expanding centers.
报告地点：维格堂319
4. 报告人 张金华（巴黎南大学,博士）
报告时间 2018年7月4日14:00-14:50,
报告题目：On theSRB measures of a partially hyperbolic attracting set withone-dimensional center
摘要：We will firstfocus on the 'unstable density basis' for partially hyperbolic attracting sets.We will definea Vitali basis in the attracting region, then we verify that it satisfiesvolumetrically engulfing property, therefore, it is an 'unstable densitybasis'.We will recall the results on theexistence of Gibbs u-states via entropy formula and the results on pseudo- physical measures.
We show that for $C^2$-partiallyhyperbolic attracting set $/Lambda$ with one-dimensional center, for Lab a.e. xin the attracting neighborhood of $/La$, either x is in the basin of ahyperbolic physical measure or the empirical measures of x consists ofnon-hyperbolic Gibbs u-states. Furthermore, in the last case, $/omega(x)$ does not support hyperbolic SRB measures. This is a joint work with S.Crovisier and D. Yang
报告地点：维格堂319
5.报告人 王晓东（上海交通大学，博士）
报告时间 2018年7月4日15:00-15:50,
报告题目：On thenon-empty interior of bi-Lyapunov stable homoclinic classes
报告摘要：We provethat for generic $f/in /diff^1(M)$, a homoclinic class $H(p)$ is bi-Lyapunovstable if and only if it contains non-empty interior. We also obtain some properties ofthe boundary of a bi-Lyapunov stable homoclinic class $H(p)$ if it does notcoincides with the whole manifold $M$. This is a joint work with S. Crovisier.
报告地点：维格堂319
2018年7月4日15:50-16:00, 茶歇
6. 报告人 王娟（上海工程技术大学，博士）
报告时间 2018年7月4日16:00-16:50,
报告题目：Hyperbolicsets for $C^1-$diffeomorphisms preserving hyperbolic measures with dominatedsplitting
报告摘要：In this paper,we consider $C^1-$diffeomorphism preserving hyperbolic measure $/mu$ whoseOseledet's splitting is dominated. There is a hyperbolic set in the smallneighborhood of the support of $/mu$.
报告地点维格堂319
2018年7月4日17:00-17:30, 讨论咨询
2018年7月5日
1. 报告人 胡虎翼（密西根州立大学,教授）
报告时间 2018年7月5日9:00-9:50,
报告题目：转移算子简介(V)
摘要：主要介绍Ruelle定义的转移算子及其在双曲动力系统中的应用
报告地点：维格堂319
2018年7月5日09:50-10:00，茶歇
2018年7月5日10:00-11:00，讨论咨询
2018年7月5日下午 离开