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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

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Mating Siegel quadratic polynomials
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by Michael Yampolsky and Saeed Zakeri
J. Amer. Math. Soc. 14 (2001), 25-78
Published electronically: October 2, 2000


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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Bibliographic 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
  • Email:,
  • Saeed Zakeri
  • Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
  • Email:
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 25-78
  • MSC (2000): Primary 37F10; Secondary 37F45, 37F50
  • DOI:
  • MathSciNet review: 1800348