Mating Siegel quadratic polynomials

Yampolsky, Michael^1, 2 ; Zakeri, Saeed³

¹ Institut des Hautes Études Scientifiques, 35 route de Chartres, F-91440, Bures-sur-Yvette, France
² Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
³ Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395

Journal of the American Mathematical Society, Tome 14 (2001) no. 1, pp. 25-78

Résumé

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 $\nu$.

Détail

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

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