Mating Siegel Quadratic Polynomials

1998/08/03 by Michael Yampolsky, Yampolsky, Michael, Saeed Zakeri +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.math/9808009

55 pages, 14 PostScript figures

arxiv created 1998/08/03 · arxiv updated 2009/11/30

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.

Citations

• A partial description of parameter space of rational maps of degree two: Part I

Cited by

• Gluing polynomials along the circle

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