报告人：糜泽亚 时间：2020.12.12 9：00-10：00 地点：泉山9#1508
个人简介
糜泽亚，理学博士，现就职于南京信息工程大学数学与统计学院。主要从事动力系统及遍历理论研究。主要研究兴趣：动力系统中SRB测度、物理测度的存在性、有限性及其统计性质。已在Math.Z, DCDS, PAMS等数学刊物上发表学术论文多篇。
报告内容
For partially hyperbolic diffeomorphism with mostly expanding and mostly contracting centers, we establish a topological structure, called skeleton. We build the one-to-one corresponding between periodic points in any skeleton and physical measures. By making perturbations on skeletons, we study the continuity of physical measures with respect to dynamics under C^1-topology.
报告人：冀诸超 时间：2020.12.12 10：30-11：30 地点：泉山9#1508
个人简介
冀诸超，博士毕业于索邦大学，导师是Romain Dujardin，主要研究方向为复动力系统（例如高维Fatou分支的分类，非一致双曲性，高维临界有限映射，高维映射的模空间上的稳定代数曲线等）。目前，在上海数学中心沈维孝老师的指导下做博士后。已在J. Geom. Anal.等期刊发表学术论文。
报告内容
Let $f$ be a holomorphic endomorphism on $\mathbb{P}^2$. The first Julia set $J_1$ is classically defined as the maximal locus such that $\left\{f^n\right\}$ locally do not form a normal family. The second Julia set $J_2\subset J_1$ is defined as the support of the measure of maximal entropy. In this talk we will study these two Julia sets for post-critically finite (PCF for short) maps. Here are two main results: 1. $J_1\setminus J_2$ is contained in the union of attracting basins of critical component cycles and stable manifolds of sporadic super-saddle points. 2. If $x\in J_2$ is not contained in the stable manifold of a sporadic super-saddle point, then there is no Fatou disk containing $x$. As corollaries of our results, 1. We answer some questions of Fornaess-Sibony about the non-wandering set for PCF maps. 2. We give a new proof of de Thelin’s laminarity of the Green current on $J_1\setminus J_2$. 3. We obtain characterizations of PCF maps which are expanding on $J_2$ or satisfy Axiom A.
报告人：邹瑞 时间：2020.12.12 14：30-15：30 地点：泉山9#1508
个人简介
邹瑞，男，苏州大学理学博士，导师为曹永罗教授。现就职于南京信息工程大学数学与统计学院。主要从事动力系统及遍历理论研究。主要研究兴趣：动力系统的上同调方程，Lyapunov指数的逼近问题等。已在 JDE,DCDS, Stoch. Dyn.等数学刊物上发表学术论文多篇。
报告内容
Let f be a non-uniformly hyperbolic system with positive entropy, and let A be a Holder continuous cocycle of injective bounded linear operators acting on a Banach space. We prove that there is a sequence of horseshoes for f and dominated splittings for A on the horseshoes, such that not only the measure theoretic entropy of f but also the Lyapunov exponents of A can be approximated by the topological entropy of f and the Lyapunov exponents of A on the horseshoes, respectively.
报告人：臧运涛 时间：2020.12.12 16：00-17：00 地点：泉山9#1508
个人简介
臧运涛，男，2020年博士毕业于苏州大学与巴黎十一大。 导师为杨大伟教授和Jerome Buzzi教授。现为华东师范大学博士后。主要研究方向为微分动力系统的遍历理论。主持博士后科学基金特别资助一项，发表论文于Nonlinearity等杂志。
报告内容
We consider a smooth diffeomorphism on a compact manifold. Ledrappier and Young introduced entropies along unstable foliations for an ergodic measure. We relate those entropies to covering numbers in order to give a new upper bound on the metric entropy in terms of Lyapunov exponents and topological entropy or volume growth of sub-manifolds.