Slowly recurrent Collet-Eckmann maps with non-empty Fatou set

Fuente: arXiv
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Main Authors: Aspenberg, Magnus, Bylund, Mats, Cui, Weiwei
Format: Preprint
Published: 2022
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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