English

On Fatou and Julia sets of foliations

Dynamical Systems 2019-09-18 v3

Abstract

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.

Keywords

Cite

@article{arxiv.1809.06767,
  title  = {On Fatou and Julia sets of foliations},
  author = {Taro Asuke},
  journal= {arXiv preprint arXiv:1809.06767},
  year   = {2019}
}

Comments

version accepted for publication in Jour. Math. Soc. Japan