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Invariant Jordan curves of Sierpinski carpet rational maps

Jinsong ZengPeter HaïssinskyYan GaoDaniel Meyer

subject

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

description

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 $R$.

yearjournalcountryeditionlanguage
2015-11-08
http://urn.fi/URN:NBN:fi:jyu-201803161744