0000000000414955

AUTHOR

Peter Haïssinsky

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Invariant Jordan curves of Sierpinski carpet rational maps

2015

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 $R$.

Mathematics::Dynamical SystemsGeneral Mathematics[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]rational functionsMathematics::General TopologyDynamical Systems (math.DS)01 natural sciences37F10Combinatoricsexpanding Thusrston mapssymbols.namesakeHigh Energy Physics::TheoryMathematics::Quantum AlgebraFOS: MathematicsMathematics::Metric GeometryMathematics - Dynamical Systems0101 mathematicsInvariant (mathematics)MathematicsmatematiikkamathematicsSierpinski carpet Julia setsApplied Mathematicsta111010102 general mathematicsinvariant Jordan curveJulia setJordan curve theoremrationaalifunktiot010101 applied mathematicsrational mapsSierpinski carpetsymbols
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