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Herman’s Condition and Siegel Disks of Bi-Critical Polynomials

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Abstract

We extend a theorem of Herman from the case of unicritical polynomials to the case of polynomials with two finite critical values. This theorem states that Siegel disks of such polynomials, under a diophantine condition (called Herman’s condition) on the rotation number, must have a critical point on their boundaries.

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Authors and Affiliations

  1. Centre National de la Recherche Scientifique, Institut de Mathématiques de Bordeaux, 351, cours de la Libération, 33405, Talence Cedex, France

    Arnaud Chéritat

  2. Institut de Mathématiques de Marseille I2M, Aix-Marseille Université, Technopôle Château-Gombert 39, rue F. Joliot Curie, 13453, Marseille Cedex 13, France

    Pascale Roesch

Authors
  1. Arnaud Chéritat
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  2. Pascale Roesch
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Correspondence to Arnaud Chéritat.

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Communicated by M. Lyubich

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Chéritat, A., Roesch, P. Herman’s Condition and Siegel Disks of Bi-Critical Polynomials. Commun. Math. Phys. 344, 397–426 (2016). https://doi.org/10.1007/s00220-016-2614-y

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  • DOI: https://doi.org/10.1007/s00220-016-2614-y

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