Asymptotically holomorphic methods for infinitely renormalizable Cr unimodal maps
File(s)CdFvS-July2022.pdf (558.8 KB)
Accepted version
Author(s)
van Strien, Sebastian
De Faria, Edson
Clark, Trevor
Type
Journal Article
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 C
r
(r > 3) 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.
deep renormalizations of asymptotically holomorphic extensions of C
r
(r > 3) 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.
Date Issued
2023-11
Date Acceptance
2022-09-09
Citation
Ergodic Theory and Dynamical Systems, 2023, 43 (11), pp.3636-3684
ISSN
0143-3857
Publisher
Cambridge University Press
Start Page
3636
End Page
3684
Journal / Book Title
Ergodic Theory and Dynamical Systems
Volume
43
Issue
11
Copyright Statement
© The Author(s), 2022. Published by Cambridge University Press. This article has been published in a revised form in Ergodic Theory and Dynamical Systems https://doi.org/10.1017/etds.2022.72. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
Identifier
https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/asymptotically-holomorphic-methods-for-infinitely-renormalizable-cr-unimodal-maps/EA14AF0D406B2015B993316569457B40
Publication Status
Published
Date Publish Online
2022-11-29