A sufficient condition for C1-smoothness of the conjugation between piecewise smooth circle homeomorphisms

H. Akhadkulov; M. S. Noorani; H. Ibrahim; S. Akhatkulov

doi:10.1215/20088752-2019-0014

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Home > Journals > Ann. Funct. Anal. > Volume 10 > Issue 4 > Article

November 2019 A sufficient condition for

C^{1}

-smoothness of the conjugation between piecewise smooth circle homeomorphisms

H. Akhadkulov, M. S. Noorani, H. Ibrahim, S. Akhatkulov

Ann. Funct. Anal. 10(4): 562-569 (November 2019). DOI: 10.1215/20088752-2019-0014

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Abstract

Let $T_{1}$ and $T_{2}$ be two piecewise smooth circle homeomorphisms with countably many break points and identical irrational rotation number. We provide a sufficient condition for $C^{1}$ -smoothness of the conjugation between $T_{1}$ and $T_{2}$ .

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H. Akhadkulov. M. S. Noorani. H. Ibrahim. S. Akhatkulov. "A sufficient condition for $C^{1}$ -smoothness of the conjugation between piecewise smooth circle homeomorphisms." Ann. Funct. Anal. 10 (4) 562 - 569, November 2019. https://doi.org/10.1215/20088752-2019-0014

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Received: 12 August 2018; Accepted: 23 February 2019; Published: November 2019

First available in Project Euclid: 29 October 2019

zbMATH: 07126073

MathSciNet: MR4026369

Digital Object Identifier: 10.1215/20088752-2019-0014

Subjects:

Primary: 37E10

Secondary: 37C15 , 37C40

Keywords: break point , circle homeomorphism , conjugation function , rotation number

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Ann. Funct. Anal.

Vol.10 • No. 4 • November 2019

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H. Akhadkulov, M. S. Noorani, H. Ibrahim, S. Akhatkulov "A sufficient condition for

C^{1}

-smoothness of the conjugation between piecewise smooth circle homeomorphisms," Annals of Functional Analysis, Ann. Funct. Anal. 10(4), 562-569, (November 2019)

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