主题：吕克宁、刘益教授系列报告

数学与统计学院、数学中心学术报告

 

时间：2011.11.30—12.2，每天上午9:30—11:30，下午2:30—5:00

 

地点：数统学院楼4楼422

 

报告人简介：

 

1. 吕克宁教授：美国Brigham Young University和Michigan State University教授, 国家杰出青年基金（B类）获得者，国家“千人计划”获得者（四川大学）。

 

2. 刘益教授：西华师大原数学学院院长。

 

两位教授都毕业于四川大学数学系（本科与硕士），方向都是偏微分方程。

 

11月30日上午：

 

Chaotic Behavior in Differential Equations Driven by a Brownian Motion(I)

 

吕克宁教授

 

Abstract: In this talk, we investigate the chaotic behavior of ordinary differential equations with a homoclinic orbit to a saddle fixed point under an unbounded random forcing driven by a Brownian motion. We prove that, for almost all sample pathes of the Brownian motion in the classical Wiener space, the forced equation admits a topological horseshoe of infinitely many branches. This result is then applied to the randomly forced Duffing equation and the pendulum equation. This is a joint work with Qiudong Wang.

 

11月30日下午：

 

Chaotic Behavior in Differential Equations Driven by a Brownian Motion(II)

 

吕克宁教授

 

时空结构的一种可能形式(I)

 

刘益教授

 

12月1日上午：

 

Lyapunov Exponents and Chaotic Behavior for Random Dynamical Systems in a Banach Space (I)

 

吕克宁教授

 

Abstract: We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. We also prove that for an infinite dimensional random dynamical system with a random invariant set such as random attractor, if it’s topological entropy is positive, then the dynamics on the random invariant set is chaotic. This is based on joint works with Wen Huang and Zeng Lian.

 

12月1日下午：

 

Lyapunov Exponents and Chaotic Behavior for Random Dynamical Systems in a Banach Space (II)

 

吕克宁教授

 

时空结构的一种可能形式(I)

 

刘益教授

 

12月2日上午：

 

Strange attractors for periodically forced parabolic equations

 

吕克宁教授

 

Abstract: We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. We also prove that for an infinite dimensional random dynamical system with a random invariant set such as random attractor, if it’s topological entropy is positive, then the dynamics on the random invariant set is chaotic. This is based on joint works with Wen Huang and Zeng Lian.

 

好多讲座，PDE威武！