Mating Siegel quadratic polynomials

Yampolsky, Michael; Zakeri, Saeed

doi:10.1090/S0894-0347-00-00348-9

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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
Posted: October 2, 2000
MathSciNet review: 1800348
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Abstract:

Let 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 Blaschke product model for the dynamics of and an adaptation of complex a priori bounds for renormalization of critical circle maps, we prove that can be realized as the mating of two Siegel quadratic polynomials with the corresponding rotation numbers $\theta$ and $\nu$ .

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