Infinite-dimensional topological dynamics: Expansivity for the Cauchy Problem

讲座题目：Infinite-dimensional topological dynamics: Expansivity for the Cauchy Problem

讲座时间 Datetime: 2025年12月8日，周一，10:00-11:00

地点 Venue: 海琴二号457

报告人Speaker: Carlos Arnoldo Morales Rojas 研究员

单位 Affiliation:Hangzhou International Innovation Institute of Beihang University

主持人 Host：Sergio Augusto Romana Ibarra副教授

报告摘要 Abstract:

We study of the topological dynamics of the affine Cauchy problem ẋ= Ax+v) on Banach spaces.

The focus is on the expansivity properties of this system. More precisely, we show that if the problem is either exponentially stable or exponentially unstable, then it is expansive on regular points. Moreover, such a problem satisfies a new form of expansivity on regular points, which we call  strong topological expansivity.

We also present basic properties of strong topologically expansive flows on metric spaces.

报告人简介：

Professor Carlos A. Morales is renowned for his foundational work in dynamical systems, particularly for his key contributions to the theory of singular-hyperbolicity, which provides a framework for analyzing complex systems like the Lorenz attractor. His influential research is published in top journals such as Annals of Mathematics, Communications in Mathematical Physics, and Transactions of the American Mathematical Society,among others.