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Bounded critical Fatou components are Jordan domains for polynomials

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Abstract

We prove that any bounded Fatou component of a polynomial of degree at least two, which is not (eventually) a Siegel disk, is a Jordan domain.

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Acknowledgements

This work was supported by Agence Nationale de la Recherche (Grant No. ANR-13-BS01-0002) and National Natural Science Foundation of China (Grant No. 11771387). The authors thank the late Professor Lei Tan and the referees for their careful reading and many helpful comments.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, 31062, France

    Pascale Roesch

  2. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Yongcheng Yin

Authors
  1. Pascale Roesch
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  2. Yongcheng Yin
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Correspondence to Yongcheng Yin.

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Roesch, P., Yin, Y. Bounded critical Fatou components are Jordan domains for polynomials. Sci. China Math. 65, 331–358 (2022). https://doi.org/10.1007/s11425-020-1827-4

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  • DOI: https://doi.org/10.1007/s11425-020-1827-4

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