Rigidity of critical circle maps

Pablo Guarino; Marco Martens; Welington De Melo

doi:10.1215/00127094-2018-0017

Rigidity of critical circle maps

Pablo Guarino
, Marco Martens
, Welington De Melo

Mathematics

Universidade Federal Fluminense
Instituto National de Matemática Pura e Aplicada

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

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 C¹circle diffeomorphism. The conjugacy is C^1+α for a full Lebesgue measure set of rotation numbers.

Original language	English
Pages (from-to)	2125-2188
Number of pages	64
Journal	Duke Mathematical Journal
Volume	167
Issue number	11
DOIs	https://doi.org/10.1215/00127094-2018-0017
State	Published - Aug 1 2018

Access to Document

10.1215/00127094-2018-0017

Cite this

@article{21d3fc4198a9441091974447145cfb2d,

title = "Rigidity of critical circle maps",

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.",

author = "Pablo Guarino and Marco Martens and \{De Melo\}, Welington",

note = "Publisher Copyright: {\textcopyright} 2018.",

year = "2018",

month = aug,

day = "1",

doi = "10.1215/00127094-2018-0017",

language = "English",

volume = "167",

pages = "2125--2188",

journal = "Duke Mathematical Journal",

issn = "0012-7094",

number = "11",

}

TY - JOUR

T1 - Rigidity of critical circle maps

AU - Guarino, Pablo

AU - Martens, Marco

AU - De Melo, Welington

PY - 2018/8/1

Y1 - 2018/8/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85051626714

U2 - 10.1215/00127094-2018-0017

DO - 10.1215/00127094-2018-0017

M3 - Article

AN - SCOPUS:85051626714

SN - 0012-7094

VL - 167

SP - 2125

EP - 2188

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 11

ER -

Rigidity of critical circle maps

Abstract

Access to Document

Other files and links

Fingerprint

Cite this