中国科学院数学与系统科学研究院

数学研究所

学术报告

复动力系统研讨班

Speaker: 曹杰 深圳大学

Title: Boundaries of capture hyperbolic components

Time & Venue: 2024.09.02（星期一）9:30-11:30 S813

Abstract:A fundamental and challenging problem in complex dynamics is to study the topological structure of

high-dimensional hyperbolic component boundaries. In this talk, we discuss the capture hyperbolic components

in polynomial families defined by periodic critical relations. We show that the boundary of a capture

hyperbolic component is homeomorphic to a high-dimensional sphere. Moreover, we establish a

relation for Hausdorff dimensions between the parameter space and the dynamical space. This is a joint

work with Prof. Xiaoguang Wang and Prof. Yongcheng Yin.

Title: Boundaries of capture hyperbolic components

Time & Venue: 2024.09.04（星期三）9:30-11:30 S813

Abstract:In this talk, we discuss the central hyperbolic component of polynomials with a fixed critical point. We

will study the dynamical properties of polynomials on the central component boundary. By introducing the

chain of Fatou components, we can give a necessary but not sufficient condition for a polynomial belonging to the

central component boundary. This is an ongoing work with Prof. Xiaoguang Wang and Prof. Yon