Invariant Jordan curves of Sierpiski carpet rational maps

Abstract

In this paper, we prove that if $R:\hat{\mathbb{C}}\to \hat{\mathbb{C}}$ is a postcritically finite rational map with Julia set homeomorphic to the Sierpiński 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 $R$.

16 pages, 1 figue

References in corpus (1)

• Persistent Markov partitions for rational maps