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Global holomorphic solutions of a generalization of the Schröder equation

Volume 244 / 2019

Yan Gao, Weinian Zhang Studia Mathematica 244 (2019), 1-24 MSC: Primary 39B32; Secondary 37F50. DOI: 10.4064/sm8780-8-2017 Published online: 14 May 2018

Abstract

We discuss global holomorphic solutions of a generalization of the Schröder equation. Necessary and sufficient conditions are given for the equation to have a holomorphic solution on a set extended from the Fatou component of an attracting or indifferent fixed point of a known function. Then we extend the result from a fixed point to a periodic point. The existence of holomorphic solutions is given by considering the complex dynamics of a known function. The continuation of holomorphic solutions is studied by investigating relations between the natural boundary of solutions and the Julia set of the known function.

Authors

  • Yan GaoDepartment of Mathematics
    Sichuan University
    Chengdu, Sichuan 610064, China
    e-mail
  • Weinian ZhangDepartment of Mathematics
    Sichuan University
    Chengdu, Sichuan 610064, China
    e-mail

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