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Invariant Jordan curves of Sierpinski carpet rational maps

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Invariant Jordan curves of Sierpinski carpet rational maps

Abstract. In this paper, we prove that if R : Cb → Cb is a postcritically finite rational map with Julia set homeomorphic to the Sierpiński carpet, then there is an integer n0, such that, for any n ≥ n0, there exists an R n -invariant Jordan curve Γ containing the postcritical set of R.

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