Imperial College London
Alternate

ProfessorSebastianvan Strien

Faculty of Natural Sciences, Department of Mathematics

Chair in Dynamical Systems
 
 
 
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Contact

 

+44 (0)20 7594 2844s.van-strien Website

 
 
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Location

 

6M36Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{van:2023:10.1017/etds.2022.72,
author = {van, Strien S and De, Faria E and Clark, T},
doi = {10.1017/etds.2022.72},
journal = {Ergodic Theory and Dynamical Systems},
pages = {3636--3684},
title = {Asymptotically holomorphic methods for infinitely renormalizable Cr unimodal maps},
url = {http://dx.doi.org/10.1017/etds.2022.72},
volume = {43},
year = {2023}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically holomorphic polynomial-like maps. Our maps arise naturally asdeep renormalizations of asymptotically holomorphic extensions of Cr(r > 3) unimodalmaps that are infinitely renormalizable of bounded type. Here we prove a version of theFatou-Julia-Sullivan theorem and a topological straightening theorem in this setting. Inparticular, these maps do not have wandering domains and their Julia sets are locallyconnected.
AU  - van,Strien S
AU  - De,Faria E
AU  - Clark,T
DO  - 10.1017/etds.2022.72
EP  - 3684
PY  - 2023///
SN  - 0143-3857
SP  - 3636
TI  - Asymptotically holomorphic methods for infinitely renormalizable Cr unimodal maps
T2  - Ergodic Theory and Dynamical Systems
UR  - http://dx.doi.org/10.1017/etds.2022.72
UR  - https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/asymptotically-holomorphic-methods-for-infinitely-renormalizable-cr-unimodal-maps/EA14AF0D406B2015B993316569457B40
UR  - http://hdl.handle.net/10044/1/99640
VL  - 43
ER  -
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