动力系统讨论班

题目:Rational dynamics on the projective line of the field of p-adic numbers

报告人：廖灵敏教授（武汉大学）

摘要：We study rational maps as dynamical systems on the projective line of the field of p-adic numbers. We usually divide the space into two invariant parts: Julia set and Fatou set. For a rational map without critical point, the subsystem on the Julia set is topologically conjugate to some subshift of finite type on an alphabet of finite symbols, i.e., finite states Markov shift, and the subsystem on the Fatou set is described by a decomposition of minimal subsystems. However, if the rational map admits critical points, its dynamical behavior becomes complicated. In general, we prove that for a geometrically finite rational map, i.e., every critical point has finite forward orbit, the dynamics on its Julia set is topologically conjugate to a countable states Markov shift. This is a joint work with Shilei Fan, Hongming Nie and Yuefei Wang.

报告时间：2024年05月08日（周三）上午10:30-11:30

报告地点：新教二楼510教室

联系人：孙善忠