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