Dynamics of Siegel Rational Maps with Prescribed Combinatorics

Details Dynamics of Siegel Rational Maps with Prescribed Combinatorics Dynamics of Siegel Rational Maps with Prescribed Combinatorics

2008-11-19

arxiv.org/abs/0811.3043v1

Mathematics

Dynamical Systems

83 Pages

Scientific paper

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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