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arXiv · 2411.14203

Piecewise quasiconformal dynamical systems of the unit circle

Yusheng Luo·Dimitrios Ntalampekos
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Abstract

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.

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Yusheng Luo, Dimitrios Ntalampekos. 2024-11-21. Piecewise quasiconformal dynamical systems of the unit circle. https://arxiv.org/abs/2411.14203

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