Dynamics and Renormalization Seminar
Wednesday December 2nd, 2020
Time: 2:30 PM - 3:30 PM
Title: mini-course: A priori bounds for neutral quadratic polynomials
Speaker: Dzmitry Dudko, Stony Brook University
Abstract:
Douady-Ghys's surgery implies that a neutral quadratic polynomial with a bounded type rotation number has a Siegel quasidisk containing the critical point on its boundary. In this minicourse, we will show that such a Siegel quasidisk degenerates in a controllable way as the rotation number becomes unbounded. This unifies (in a certain sense) the Inou-Shishikura near-parabolic and the Pacman near-Siegel renormalization theories for neutral quadratic polynomials (parametrized by the main cardioid).
Joint work with Misha Lyubich.
The first lecture will give a general introduction to the near-neutral renormalization theories. We will also outline the main steps of proving the new a priori bounds and discuss some consequences previously known only in the Innou-Shishikura class.Â