Mating Siegel Quadratic Polynomials

Details Mating Siegel Quadratic Polynomials Mating Siegel Quadratic Polynomials

1998-08-03

arxiv.org/abs/math/9808009v1

Mathematics

Dynamical Systems

55 pages, 14 PostScript figures

Scientific paper

Let F be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers theta and nu. Using a new degree 3 Blaschke product model for the dynamics of F and an adaptation of complex a priori bounds for renormalization of critical circle maps, we prove that F can be realized as the mating of two Siegel quadratic polynomials with the corresponding rotation numbers theta and nu.

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