Invariant Jordan curves of Sierpiski carpet rational maps



Gao, Yan, Haïssinsky, Peter, Meyer, Daniel and Zeng, Jinsong
(2015) Invariant Jordan curves of Sierpiski carpet rational maps. Ergodic Theory and Dynamical Systems, 38 (2). pp. 583-600.

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Abstract

In this paper, we prove that if $R\colon\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ is a postcritically finite rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there is an integer $n_0$, such that, for any $n\ge n_0$, there exists an $R^n$-invariant Jordan curve $\Gamma$ containing the postcritical set of $R$.

Item Type: Article
Additional Information: 16 pages, 1 figue
Uncontrolled Keywords: math.DS, math.DS, 37F10
Depositing User: Symplectic Admin
Date Deposited: 10 Dec 2018 10:54
Last Modified: 19 Jan 2023 01:09
DOI: 10.1017/etds.2016.47
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3029820