Dynamics of asymptotically holomorphic polynomial-like maps
Dynamical Systems
2018-04-18 v1
Abstract
The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of asymptotically holomorphic extensions of () unimodal maps that are infinitely renormalizable of bounded type. Here we prove a version of the Fatou-Julia-Sullivan theorem and a topological straightening theorem in this setting. In particular, these maps do not have wandering domains and their Julia sets are locally connected.
Keywords
Cite
@article{arxiv.1804.06122,
title = {Dynamics of asymptotically holomorphic polynomial-like maps},
author = {Trevor Clark and Edson de Faria and Sebastian van Strien},
journal= {arXiv preprint arXiv:1804.06122},
year = {2018}
}
Comments
47 pages