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October, 2020 On Fatou and Julia sets of foliations
Taro ASUKE
J. Math. Soc. Japan 72(4): 1145-1159 (October, 2020). DOI: 10.2969/jmsj/81338133

Abstract

The Fatou–Julia decomposition is significant in the study of iterations of holomorphic mappings. Such a decomposition has been considered for foliations in a unified manner by Ghys–Gomez-Mont–Saludes, Haefliger, the author, et al. Although the decomposition will be fundamental in the study, it is not easy to determine 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.

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Taro ASUKE. "On Fatou and Julia sets of foliations." J. Math. Soc. Japan 72 (4) 1145 - 1159, October, 2020. https://doi.org/10.2969/jmsj/81338133

Information

Received: 25 September 2018; Revised: 1 May 2019; Published: October, 2020
First available in Project Euclid: 11 March 2020

MathSciNet: MR4165926
Digital Object Identifier: 10.2969/jmsj/81338133

Subjects:
Primary: 37F75
Secondary: 32S65, 57R30

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 4 • October, 2020
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