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Topological characterisation of rational maps with Siegel disks

Part of: Complex dynamical systems

Published online by Cambridge University Press:  10 February 2021

GAOFEI ZHANG
GAOFEI ZHANG*
Affiliation:
Department of Mathematics, Qufu Normal University, Jing Xuan West Road, No. 57, Qufu, Shan Dong, P. R. China, 273165. e-mail: zhanggf@hotmail.com
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Abstract

We extend Thurston’s topological characterisation theorem for postcritically finite rational maps to a class of rational maps which have a fixed bounded type Siegel disk. This makes a small step towards generalizing Thurston’s theorem to geometrically infinite rational maps.

MSC classification

Primary: 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
Secondary: 37F20: Combinatorics and topology 37F10: Polynomials; rational maps; entire and meromorphic functions
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 1 , January 2022 , pp. 1 - 41
Copyright
© Cambridge Philosophical Society 2021

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