12月12日 动力系统系列学术报告(数学与统计学院)

时间:2020-12-10浏览:47设置

报告时间:2020年12月12日(周六)时间:9:00-11:30  14:30-17:00

活动地点:泉山9#1508

主办单位:数学与统计学院、科学与技术研究院


报告人:糜泽亚  

报告题目SRB measures and skeletons for maps with mostly expanding and mostly contracting centers

报告人简介:

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。

报告摘要

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  

报告题目Julia sets of 2-dimensional post-critically finite maps

报告人简介

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。

报告摘要

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

报告题目:Horseshoes and Lyapunov exponents for Banch cocycles

报告人简介:

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。 

报告摘要

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

报告题目:Entropies and volume growth of unstable manifolds

报告人简介:

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

报告摘要

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.


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