Piecewise quasiconformal dynamical systems of the unit circle

Fuente: arXiv
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Hauptverfasser: Luo, Yusheng, Ntalampekos, Dimitrios
Format: Preprint
Veröffentlicht: 2024
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author Luo, Yusheng
Ntalampekos, Dimitrios
author_facet Luo, Yusheng
Ntalampekos, Dimitrios
contents We study piecewise quasiconformal covering maps of the unit circle. We provide sufficient conditions so that a conjugacy between two such dynamical systems has a quasiconformal or David extension to the unit disk. Our main result generalizes the main result of arXiv:2010.11256, which deals with piecewise analytic maps. As applications, we provide a classification of piecewise quasiconformal maps of the circle up to quasisymmetric conjugacy, we prove a general conformal mating theorem for Blaschke products, and we study the quasiconformal geometry of parabolic basins.
format Preprint
id arxiv_https___arxiv_org_abs_2411_14203
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Piecewise quasiconformal dynamical systems of the unit circle
Luo, Yusheng
Ntalampekos, Dimitrios
Dynamical Systems
Complex Variables
Primary 30J10, 37F10, 37F31, Secondary 30C62, 30C65
We study piecewise quasiconformal covering maps of the unit circle. We provide sufficient conditions so that a conjugacy between two such dynamical systems has a quasiconformal or David extension to the unit disk. Our main result generalizes the main result of arXiv:2010.11256, which deals with piecewise analytic maps. As applications, we provide a classification of piecewise quasiconformal maps of the circle up to quasisymmetric conjugacy, we prove a general conformal mating theorem for Blaschke products, and we study the quasiconformal geometry of parabolic basins.
title Piecewise quasiconformal dynamical systems of the unit circle
topic Dynamical Systems
Complex Variables
Primary 30J10, 37F10, 37F31, Secondary 30C62, 30C65
url https://arxiv.org/abs/2411.14203