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. |