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On the structure of Fatou domains

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Abstract

Let U be a multiply-connected fixed attracting Fatou domain of a rational map f. We prove that there exist a rational map g and a completely invariant Fatou domain V of g such that (f,U) and (g,V) are holomorphically conjugate, and each non-trivial Julia component of g is a quasi-circle which bounds an eventually superattracting Fatou domain of g containing at most one postcritical point of g. Moreover, g is unique up to a holomorphic conjugation.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    GuiZhen Cui & WenJuan Peng

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  1. GuiZhen Cui
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  2. WenJuan Peng
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Correspondence to WenJuan Peng.

Additional information

This work was supported by the National Basic Research Programme of China (Grant No. 2006CB805903) and the National Natural Science Foundation of China (Grant No. 10421101)

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Cui, G., Peng, W. On the structure of Fatou domains. Sci. China Ser. A-Math. 51, 1167–1186 (2008). https://doi.org/10.1007/s11425-008-0056-5

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  • DOI: https://doi.org/10.1007/s11425-008-0056-5

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