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Invariant Jordan curves of Sierpiński carpet rational maps
Published online by Cambridge University Press: 09 September 2016
Abstract
In this paper, we prove that if $R:\widehat{\mathbb{C}}\rightarrow \widehat{\mathbb{C}}$ 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
$n\geq n_{0}$, there exists an
$R^{n}$-invariant Jordan curve
$\unicode[STIX]{x1D6E4}$ containing the postcritical set of
$R$.
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- © Cambridge University Press, 2016
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