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

Abstract

We prove that any two C4 critical circle maps with the same irrational rotation number and the same odd criticality are conjugate to each other by a C1 circle diffeomorphism. The conjugacy is C1+α for a full Lebesgue measure set of rotation numbers.

Citation

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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

Information

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

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 11 • 15 August 2018
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