Collet-Eckmann type conditions and conformal welding of unicritical quadratic laminations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916720416915456 |
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| 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 |