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

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.

Domaines: Systèmes dynamiques [math.DS]

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