Chennai Mathematical Institute

Seminars




Mathematics Seminar
Date: Monday, 21 August 2023
Time: 3:30 PM
Venue: Lecture Hall 1
Fatou-Bieberbach domains and attracting basins

Sayani Bera
Indian Association for the Cultivation of Science.
21-08-23


Abstract

Fatou-Biberbach domains in $\mathbb{C}^k, k \ge 2$ are proper subdomains of $\mathbb{C}^k, k \ge 2$ that are biholomorphic to $\mathbb{C}^k, k \ge 2$. Such domains clearly do not exist in $\mathbb{C}$ and, further arise naturally from dynamics of automorphisms of $\mathbb{C}^k, k \ge 2$, admitting an attracting fixed point. The goal of this talk is to discuss a few pathological examples of such domains, and also their relevance in the context of geometry, complex function theory and dynamics.

Further, we will introduce non-autonomous (dynamical) families and their basins attractions, and discuss an affirmative solution to a long standing open problem, called the Bedford's conjecture, related to the (non-autonomous) dynamical origins of a Fatou-Bieberbach domain. This is a joint work with Dr. Kaushal Verma.