Structurally stable homoclinic classes
报告题目：Structurally stable homoclinic classes
报告题目：Structurally stable homoclinic classes
报告人： 文晓（北京航空航天大学）
报告时间：2016年4月24日（周日）上午10：00-11：00
报告地点：维格堂319
报告摘要： In the talk the hyperbolicity of structurally stable homoclinic classes is showed. In a intrinsic way, the structural stability for an individual homoclinic class can be defined through the continuation of periodic points.
Since the homoclinic class is not innately locally maximal, it is hard to answer whether structurally stable homoclinic classes are hyperbolic. In the talk, we will show that if a homoclinic class is structurally stable, then it admits a dominated splitting. And also we will show that if a structurally stable classes also admit the shadowing property, then it is hyperbolic.
By a recent work of Xiaodong Wang, we can answer that every structurally stable homoclinic classes are hyperbolic
报告题目： Poincar‘e Section Map for Lipshitz Vector Fields
报告人： 文晓（北京航空航天大学）报告时间：2016年4月25日（周一）上午10：00-11：00
报告地点：维格堂319报告摘要： Poincar‘e section map is an important tool to study the continuous time differential dynamical system. It is well kown that Lipshitz vecter field can also generate a flow in a Banach space. In the talk, the Poincar‘e section map for a Lipshitz vector field is introduced. We will show that the definition domain of the Lipshitz vector field has a uniform size. We will also show that the Poincar‘e section map is lipeomorphism with a universal Lipshitz constants depends on the Lipshitz constant of vecter field and the time.