Rigidity of critical circle maps

Pablo Guarino; Marco Martens; Welington de Melo

doi:10.1215/00127094-2018-0017

Abstract

We prove that any two $C^{4}$ critical circle maps with the same irrational rotation number and the same odd criticality are conjugate to each other by a $C^{1}$ circle diffeomorphism. The conjugacy is $C^{1+\alpha}$ for a full Lebesgue measure set of rotation numbers.

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Pablo Guarino. Marco Martens. Welington de Melo. "Rigidity of critical circle maps." Duke Math. J. 167 (11) 2125 - 2188, 15 August 2018. https://doi.org/10.1215/00127094-2018-0017

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Received: 15 December 2016; Revised: 19 March 2018; Published: 15 August 2018

First available in Project Euclid: 18 July 2018

zbMATH: 06941819

MathSciNet: MR3843373

Digital Object Identifier: 10.1215/00127094-2018-0017

Subjects:

Primary: 37E10

Secondary: 37E20

Keywords: commuting pairs , critical circle maps , renormalization , smooth rigidity

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