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Mating Siegel quadratic polynomials

Authors: Michael Yampolsky and Saeed Zakeri
Journal: J. Amer. Math. Soc. 14 (2001), 25-78
MSC (2000): Primary 37F10; Secondary 37F45, 37F50
Published electronically: October 2, 2000
MathSciNet review: 1800348
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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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Additional Information

Michael Yampolsky
Affiliation: Institut des Hautes Études Scientifiques, 35 route de Chartres, F-91440, Bures-sur-Yvette, France
Address at time of publication: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3

Saeed Zakeri
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395

Keywords: Holomorphic dynamics, rational map, Siegel disk, mating, Julia set
Received by editor(s): March 25, 1999
Received by editor(s) in revised form: June 9, 2000
Published electronically: October 2, 2000
Additional Notes: The first author was partially supported by NSF grant DMS-9804606
Article copyright: © Copyright 2000 American Mathematical Society