Introduction to complex dynamics: from ”critical” point of view

Thời gian: 14:30 đến 16:30 ngày 31/10/2023, 14:30 đến 16:30 ngày 07/11/2023,

Địa điểm: B102, VIASM

Speaker: TS. Lê Văn Tứ

Abstract: This is the first talk of a series of two talks. I will introduce some basic notions of complex dynamics of rational maps, i.e. holomorphic self-map of 𝐶̂. More precisely, given a rational map f of degree d ≥ 2, I will focus on the study of the local behavior near a periodic cycle by using the multiplier, and how this local behavior affects the global behavior of f. Roughly speaking, these are under control by the dynamics of critical points. In a special case, when every critical point is either periodic or preperiodic, f is called post-critically finite. I will present how we can generalize this notion in higher dimension and how to construct some important families of post-critically finite maps in higher dimension.