Taro Asuke
Published 2018-09-18Version 1
The Fatou-Julia decomposition is significant in the study of iterations of holomorphic mappings. Such a decomposition can be also considered for foliations in a unified manner. Although the decomposition will be fundamental in the study, it is not easy to decide the decomposition. In this article, we give a sufficient condition for open sets to be contained in Fatou sets. We also discuss relations between Fatou--Julia decompositions and minimal sets.
Interior Dynamics of Fatou Sets
Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn
Meromorphic functions whose action on their Julia sets is non-ergodic
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