Piecewise smoothness of conjugate homeomorphisms of a circle with corners
type: Item
instance of: scholarly article
title: Piecewise smoothness of conjugate homeomorphisms of a circle with corners
zbMATH Open document ID: 0988.37046
DOI: 10.1007/BF02557404
published in: Theoretical and Mathematical Physics
publication date: 2002-07-22T00:00:00Z
review text: The paper deals with dynamical properties of circle homeomorphisms with corners, that is maps that are smooth everywhere except several singularities where the first derivative is discontinuous. The author considers the orientation-preserving homeomorphism \(T_fx\) of the unit circle, \[ T_fx= \{f(x)\}_f, \qquad x\in S^1= [0,1), \] where the braces denote the fractional part of a number and \(f(x)\) is a pullback determining \(T_f\). Under some natural conditions on \(f\), he studies the renormalization group behaviour and proves its convergence to linear transformations.
Mathematics Subject Classification ID: 37E10
Mathematics Subject Classification ID: 37C15
zbMATH DE Number: 1465898
zbMATH Keywords: rotation number
zbMATH Keywords: circle homeomorphisms
zbMATH Keywords: singularities
zbMATH Keywords: renormalization group
author: A. A. Dzhalilov
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q4746033
cites work: Sur les courbes definies par les équations différentielles à la surface du tore
cites work: Small denominators. I. Mappings of the circumference onto itself
cites work: Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
cites work: Automorphisms of compact groups
cites work: A new proof of M. Herman's theorem
cites work: Smoothness of conjugacies of diffeomorphisms of the circle with rotations
cites work: Smooth conjugacy and renormalisation for diffeomorphisms of the circle
cites work: Homeomorphisms of the circle with singularities of “break” type
cites work: On an invariant measure for homeomorphisms of the circle with a single break point
description: scientific article; zbMATH DE number 1465898