Collet-Eckmann type conditions and conformal welding of unicritical quadratic laminations

Fuente: arXiv
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Main Author: Huang, Linhang
Format: Preprint
Published: 2025
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_version_ 1866916720416915456
author Huang, Linhang
author_facet Huang, Linhang
contents In this paper, we introduce a Collet-Eckmann type condition for the unicritical laminations on the unit circle. We prove that this condition implies the lamination admits a Hölder continuous conformal welding which produces a Julia set for some unicritical polynomial. In consequence, we present a new proof that almost all angles on the unit circle produce quadratic polynomials with Hölder Fatou components, without the use of Beurling's theorem.
format Preprint
id arxiv_https___arxiv_org_abs_2505_02965
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Collet-Eckmann type conditions and conformal welding of unicritical quadratic laminations
Huang, Linhang
Dynamical Systems
Complex Variables
In this paper, we introduce a Collet-Eckmann type condition for the unicritical laminations on the unit circle. We prove that this condition implies the lamination admits a Hölder continuous conformal welding which produces a Julia set for some unicritical polynomial. In consequence, we present a new proof that almost all angles on the unit circle produce quadratic polynomials with Hölder Fatou components, without the use of Beurling's theorem.
title Collet-Eckmann type conditions and conformal welding of unicritical quadratic laminations
topic Dynamical Systems
Complex Variables
url https://arxiv.org/abs/2505.02965