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arXiv · 2505.02965

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

Linhang Huang
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Abstract

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 H\"older 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 H\"older Fatou components, without the use of Beurling's theorem.

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Linhang Huang. 2025-05-05. Collet-Eckmann type conditions and conformal welding of unicritical quadratic laminations. https://arxiv.org/abs/2505.02965

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