A characterization of Sierpiński carpet rational maps

Yan Gao; Jinsong Zeng; Suo Zhao

doi:10.3934/dcds.2017218

Article Contents

2017, Volume 37, Issue 9: 5049-5063. Doi: 10.3934/dcds.2017218

This issue Previous Article Global solution for the $3D$ quadratic Schrödinger equation of $Q(u, \bar{u}$) type Next Article

A characterization of Sierpiński carpet rational maps

1.
Mathematical School of Sichuan University, Chengdu 610065, China
2.
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
3.
Guosen Securities Co., Ltd. Postdoctoral Workstation, Shenzhen 518001, China

* Corresponding author
* Corresponding author

Received: March 2016

Revised: April 2017

Published: October 2017

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Abstract

In this paper we prove that a postcritically finite rational map with non-empty Fatou set is Thurston equivalent to an expanding Thurston map if and only if its Julia set is homeomorphic to the standard Sierpiński carpet.

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Mathematics Subject Classification: Primary: 37F10; Secondary: 37F45.

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References

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