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arXiv · 1511.02457

Invariant Jordan curves of Sierpiski carpet rational maps

Yan Gao·Peter Haïssinsky·Daniel Meyer·Jinsong Zeng
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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 $R$.

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Yan Gao, Peter Haïssinsky, Daniel Meyer, Jinsong Zeng. 2015-11-08. Invariant Jordan curves of Sierpiski carpet rational maps. https://arxiv.org/abs/1511.02457

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