时间：2021年6月5日8：40-17：40

地点：吴中全季酒店多功能厅

报告人：陈二才

题目：Mean Chaos and Multifractal Analysis in Symbolic Systems

摘要：In this talk, we will show that we can use multifractal analysis to investigate the mean chaotic phenomena in dynamical systems.

报告人：史恩慧

题目：Group actions on curves

摘要：In this talk, we will discuss some classical results and recent developments in the theory of group actions on curves and will focus on the structure and classification of subgroups of curve homeomorphism groups . Some open questions are also introduced.

报告人：周小敏

题目：Measure complexity and Rigid systems

摘要：We give an equivalent characterization of rigid measure preserving systems by the two metrics. It turns out that an invariant measure on a topological dynamical system has bounded complexity with respect to the two metrics if and only if system is rigid. We also obtain computation formulas of the measure-theoretic entropy of an ergodic measure preserving system (resp. the topological entropy of a topological dynamical system) by the two metrics.

报告人：邹瑞

题目：Livsic theorems for Banach cocycles: existence and regularity

摘要：We prove a nonuniformly hyperbolic version Livsic theorem, with cocycles taking values in the group of invertible bounded linear operators on a Banach space. The result holds without the ergodicity assumption of the hyperbolic measure. Moreover, We also prove a \mu-continuous solution of the cohomological equation is actually Holder continuous for the uniform hyperbolic system.

报告人：连增

题目：Chaotic behavior of hyperbolic dynamical systems

摘要：In this talk, we will report some recent progress of the study on chaotic behavior of hyperbolic dynamical systems, which mainly contains two parts: (1)Existence of periodic orbits and Smale horseshoes; (2) Ergodic optimization theory. This is based on the joint works with Wen Huang, Kening Lu, Xiao Ma, Leiye Xu, Lai-sang Young, and Yiwei Zhang.

报告人：臧运涛

题目：Topological entropy of partially hyperbolic systems with multi 1-D centers

摘要:We consider a $C^1$ partially hyperbolic diffeomorphism on a compact manifold with multi 1-D centers. We prove an entropy formula w.r.t. the volume growth rate of subspaces in the tangent bundle.

报告人：王娟

题目： The approximation of uniform hyperbolicity for diffeomorphisms preserving hyperbolic measures

摘要：For a $C^{1+\alpha}$ diffeomorphism $f$ preserving a hyperbolic ergodic SRB measure $\mu$, Katok's remarkable results assert that $\mu$ can be approximated by a sequence of hyperbolic sets $\{\Lambda_n\}_{n\geq1}$. In this work, we prove the Hausdorff dimension for $\Lambda_n$ on the unstable manifold tends to the dimension of the unstable manifold. Furthermore, if the stable direction is one dimension, then the Hausdorff dimension of $\mu$ can be approximated by the Hausdorff dimension of $\Lambda_n$. We also extend Katok's remarkable results to $C^1$ diffeomorphisms with dominated splitting.

报告人：窦斗

题目：Weighted SMB theorem and weighted entropy for amenable group actions

摘要：In 2016, Feng and Huang setup the theory of weighted entropy and pressure for finite many factor systems. In this talk, we consider weighted entropy for countable discrete amenable group actions. By giving suitable definitions of weighted partition and weighted Bowen ball, we prove a weighted version of SMB theorem and variational principle for entropy.