Speaker: 曹杰，深圳大学

Inviter: 彭文娟研究员

Title: Boundaries of capture hyperbolic components

Language: Chinese

Time & Venue: 2024.09.02 09:30-11:30 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.