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Mating Siegel Quadratic Polynomials

Michael Yampolsky·Saeed Zakeri
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Abstract

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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Michael Yampolsky, Saeed Zakeri. 1998-08-03. Mating Siegel Quadratic Polynomials. https://arxiv.org/abs/math/9808009

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