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Invariant Jordan curves of Sierpiski carpet rational maps

Yan Gao 1 Peter Haïssinsky 2, 3 Daniel Meyer Jinsong Zeng 4
1 SCU - Sichuan University [Chengdu]
2 I2M - Institut de Mathématiques de Marseille
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
Abstract : In this paper, we prove that if R:Cˆ→Cˆ is a postcritically finite rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there is an integer n0, such that, for any n≥n0, there exists an Rn-invariant Jordan curve Γ containing the postcritical set of R.
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https://hal.archives-ouvertes.fr/hal-01228363
Contributor : Peter Haïssinsky <>
Submitted on : Friday, November 13, 2015 - 8:31:33 AM
Last modification on : Wednesday, June 9, 2021 - 10:00:09 AM

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CHL | CNRS | UNIV-ANGERS | INSMI | IMT | UNIV-TLSE2 | TDS-MACS | FMPL | EC-MARSEILLE | I2M-2014- | I2M | UNIV-AMU | UNIV-TLSE3 | UT1-CAPITOLE | INSA-TOULOUSE | INSA-GROUPE | LAREMA

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Yan Gao, Peter Haïssinsky, Daniel Meyer, Jinsong Zeng. Invariant Jordan curves of Sierpiski carpet rational maps. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2018, 38 (2), pp.583 -- 600. ⟨10.1017/etds.2016.47⟩. ⟨hal-01228363⟩

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