Friday December 4th, 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. In the second lecture, we will overview principles of the near-degenerate regime and show how the Covering Lemma can be applied to Siegel maps. We will then discuss a mechanism of how a priori bounds' failure on a given scale can lead to even bigger failure on a deeper scale. | |