|
|
Knots, Graphs and Groups seminar
4 октября 2025 г. 17:05–18:35, г. Москва
|
 |
|
 |
|
|
|
[Renormalization, equipotential annuli, and the Hausdorff measure]
В. А. Тиморин |
|
Аннотация:
(based on a joint work with A. Blokh, G. Levin, and L. Oversteegen)
For a complex single variable polynomial f of degree d, let K(f) be its filled Julia set, i.e., the union of all bounded orbits. Assume that K(f) has an invariant component K* on which f acts as a degree d*<d map. This is a simplest instance of holomorphic polynomial-like renormalization (Douady-Hubbard): the dynamics of a higher degree (degree d) polynomial f near K* can be understood in terms of a suitable lower degree (degree d*) polynomial to which the restriction of f to K* is semiconjugate. One can associate a certain Cantor-like subset G’ of the circle with K*; the latter is defined in a combinatorial way. We will describe a role the Hausdorff dimension of G’ and the respective Hausdorff measure play in geometry of K*.
Язык доклада: английский
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
|
|
Обратная связь: