题目：SRB measures for partially hyperbolic expanding flows II-mostly contracting case, Part I

报告人：糜泽亚 （南京信息工程大学）

时间：2020年11月28日09：00-9：50

地点：纯水楼301

摘要：For a partially hyperbolic system with mostly contacting centers, we prove the finiteness of SRB/physical measures and with basin covering property. 

题目：SRB measures for partially hyperbolic expanding flows II-mostly contracting case, Part II

报告人：糜泽亚 （南京信息工程大学）

时间：2020年11月28日10：00 - 11:00

地点：纯水楼301

摘要：For a partially hyperbolic system with mostly contacting centers, we establish the statistical stability of this kind of flows.

题目：Continuity of subadditive topological pressure，Part I

报告人：邹瑞（南京信息工程大学）

时间：2020年11月28日11：00-11:50

地点：纯水楼301

摘要：Let f be a totally non-uniformly hyperbolic system。and let A be a Holder continuous cocycle of injective bounded linear operators acting on a Banach space with A(x) compact and injective everywhere .  We introduce the definitions and basic properties of the topological pressure of the singular value potentials.

题目：Continuity of subadditive topological pressure，Part II

报告人：邹瑞（南京信息工程大学）

时间：2020年11月28日13：30-14:20

地点：纯水楼301

摘要：For a Holder continuous cocycle A of injective bounded linear operators over a totally non-uniformly hyperbolic system, we prove that the topological pressure of the singular value potentials is continuous at A.

题目：Dimension theory of uniform Diophantine approximation related to Beta-transformations, Part I

报告人：吴万楼 （江苏师范大学）

时间：2020年11月28日14：30-15：20

地点：纯水楼301

摘要：For $\beta>1$, let $T_\beta$ be the $\beta$-transformation defined on $[0,1)$. We study the sets of points whose orbits of $T_\beta$ have uniform Diophantine approximation properties. Precisely, for two given positive functions  $\psi_1,~\psi_2:\mathbb{N}\rightarrow\mathbb{R}^+$, define $$\mathcal{L}(\psi_1):=\left\{x\in[0,1]:T_\beta^n x<\psi_1(n),\text{for infinitely many $n\in\mathbb{N}$}\right\},$$ $$\mathcal{U}(\psi_2):=\left\{x\in [0,1]:\forall~N\gg1,~\exists~n\in[0,N],~s.t.~T^n_\beta x<\psi_2(N)\right\},$$ where $\gg$ means large enough. We calculate the Hausdorff dimension of the set $\mathcal{L}(\psi_1)\cap\mathcal{U}(\psi_2)$. 

题目：Dimension theory of uniform Diophantine approximation related to Beta-transformations, Part II

报告人：吴万楼 （江苏师范大学）

时间：2020年11月28日14：30-15：20

地点：纯水楼301

摘要：For $\beta>1$, let $T_\beta$ be the $\beta$-transformation defined on $[0,1)$.  For two given positive functions  $\psi_1,~\psi_2:\mathbb{N}\rightarrow\mathbb{R}^+$, define

$$\mathcal{L}(\psi_1):=\left\{x\in[0,1]:T_\beta^n x<\psi_1(n),\text{for infinitely many $n\in\mathbb{N}$}\right\},$$ $$\mathcal{U}(\psi_2):=\left\{x\in [0,1]:\forall~N\gg1,~\exists~n\in[0,N],~s.t.~T^n_\beta x<\psi_2(N)\right\},$$ We obtain the Hausdorff dimension of the set $\mathcal{U}(\psi_2)$. Our work generalizes the results of Bugeaud and Liao where only exponential functions $\psi_1,~\psi_2$ were taken into consideration..

题目：Uniform Diophantine approximation related to beta-transformations 

报告人：吴万楼 （江苏师范大学）

时间：2020年11月28日16：30-17：20

地点：纯水楼301

摘要：For any $\beta>1$, let $T_\beta$ be the classical $\beta$-transformations. Fix $x_0\in[0,1]$ and a nonnegative real number $\hat{v}$, we compute the Hausdorff dimension of the set of real numbers $x\in[0,1]$ with the property that, for every sufficiently large integer $N$, there is an integer $n$ with $1\leq n\leq N$ such that the distance between $T_\beta^nx$ and $x_0$ is at most equal to $\beta^{-N\hat{v}}$.