Dynamics of Siegel Rational Maps with Prescribed Combinatorics

2008/11/19 by Gaofei Zhang, Zhang, Gaofei · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.CV #math.DS #msc:37F10 #msc:58F23

paper · pdf · doi:10.48550/arxiv.0811.3043

83 Pages

arxiv created 2008/11/19 · arxiv updated 2009/12/01

Abstract

We extend Thurston's combinatorial criterion for postcritically finite rational maps to a class of rational maps with bounded type Siegel disks. The combinatorial characterization of this class of Siegel rational maps plays a special role in the study of general Siegel rational maps. As one of the applications, we prove that for any quadratic rational map with a bounded type Siegel disk, the boundary of the Siegel disk is a quasi-circle which passes through one or both of the critical points.

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