Global holomorphic solutions of a generalization of the Schröder equation
Volume 244 / 2019
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.
