Rigidity for circle homeomorphisms with a break-type singularity
type: Item
instance of: scholarly article
title: Rigidity for circle homeomorphisms with a break-type singularity
zbMATH Open document ID: 0967.37026
published in: Doklady Mathematics
publication date: 2001-02-13T00:00:00Z
review text: Let \(f\) be a smooth except for one point homeomorphism of a circle \(f\in C^{2+\varepsilon}(S^1\setminus\{x_0\})\), with existing one-sided derivatives at \(x_0\). Let \(c(f)=\sqrt{f'_{-}(x_0)/f'_{+}(x_0)}\) and \(\rho(f)\) be the rotation number. Theorem: If \(f\) and \(h\) are such that \(c(f)=c(h)\not=1\) and \(\rho(f)=\rho(h)\) is irrational with periodic continued fraction expansion then there exists a \(\delta>0\) such that \(f\) and \(g\) are \(C^{1+\delta}\) conjugate. Conjecture. The assumption on periodic expansion can be omitted.
reviewed by: Tomasz Nowicki
Mathematics Subject Classification ID: 37E10
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 37E45
zbMATH DE Number: 1564539
zbMATH Keywords: circle maps
zbMATH Keywords: class of conjugacy smoothness
zbMATH Keywords: rigidity
author: K. Khanin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1564539