Slowly recurrent Collet-Eckmann maps with non-empty Fatou set
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914705806721024 |
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| author | Aspenberg, Magnus Bylund, Mats Cui, Weiwei |
| author_facet | Aspenberg, Magnus Bylund, Mats Cui, Weiwei |
| contents | In this paper we study rational Collet-Eckmann maps for which the Julia set is not the whole sphere and for which the critical points are recurrent at a slow rate. In families where the orders of the critical points are fixed, we prove that such maps are Lebesgue density points of hyperbolic maps. In particular, if all critical points are simple, they are Lebesgue density points of hyperbolic maps in the full space of rational maps of any degree $d \geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14046 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Slowly recurrent Collet-Eckmann maps with non-empty Fatou set Aspenberg, Magnus Bylund, Mats Cui, Weiwei Dynamical Systems 37F10, 37F15, 30D05 In this paper we study rational Collet-Eckmann maps for which the Julia set is not the whole sphere and for which the critical points are recurrent at a slow rate. In families where the orders of the critical points are fixed, we prove that such maps are Lebesgue density points of hyperbolic maps. In particular, if all critical points are simple, they are Lebesgue density points of hyperbolic maps in the full space of rational maps of any degree $d \geq 2$. |
| title | Slowly recurrent Collet-Eckmann maps with non-empty Fatou set |
| topic | Dynamical Systems 37F10, 37F15, 30D05 |
| url | https://arxiv.org/abs/2207.14046 |