Dynamics of transcendental H\'enon maps-II
Dynamical Systems
2019-05-29 v1 Complex Variables
Abstract
Transcendental H\'enon maps are the natural extensions of the well investigated complex polynomial H\'enon maps to the much larger class of holomorphic automorphisms. We prove here that transcendental H\'enon maps always have non-trivial dynamical behavior, namely that they always admit both periodic and escaping orbits, and that their Julia sets are non-empty and perfect.
Keywords
Cite
@article{arxiv.1905.11557,
title = {Dynamics of transcendental H\'enon maps-II},
author = {Leandro Arosio and Anna Miriam Benini and John Erik Fornæss and Han Peters},
journal= {arXiv preprint arXiv:1905.11557},
year = {2019}
}