Speaker: Mikhail Lyubich, Stony Brook University
January 8, 2024 09:30 AM
- 10:30 AM
Abstract:
We will discuss an interplay between three branches of Conformal Dynamics: iterations of (anti-)rational maps, action of Kleinian reflection groups, and dynamics generated by Schwarz reflections in quadrature domains. We will show how David surgery can turn one set on this list to another (for instance, the classical Apollonian gasket into a Julia set). It also allows one to mate Julia sets with Kleinian limit sets obtaining a set generated by Schwarz reflections (for instance, one can mate an anti-holomorphic quadratic polynomial with the modular group). Interesting examples of removable fractals can be obtained in this way. Time permitted, we will discuss relations between the corresponding parameter spaces.
Based on a series of works with Russell Lodge, Nick Makarov, Sergiy Merenkov, Sabya Mukherjee, Dimitrios Ntalampekos, and other people.