Rigidity and renormalization in one dimensional dynamical systems
type: Item
instance of: scholarly article
title: Rigidity and renormalization in one dimensional dynamical systems
zbMATH Open document ID: 0914.58016
published in: Documenta Mathematica
publication date: 1998-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/229001
full work available at URL: Demelo.MAN.html
review text: This article reviews the recent development in the renormalization theory of unimodal maps and critical circle maps. If two smooth unimodal maps or real analytic critical circle maps have the same bounded combinatorial type, then there exists a \(C^{1+\alpha}\) diffeomorphism conjugating the two maps along the corresponding critical orbit for some \(\alpha>0\). The article gives an overview of the proof which is based on a detailed understanding of the orbit structure of infinite-dimensional dynamical systems: the renormalization operator.
reviewed by: Yunping Jiang
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 1184286
zbMATH Keywords: infinite renormalization
zbMATH Keywords: rigidity
zbMATH Keywords: unimodal maps
zbMATH Keywords: critical circle maps
zbMATH Keywords: renormalization operator
author: Welington de Melo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1184286