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Moscow Mathematical Journal, 2014, Volume 14, Number 2, Pages 367–384
DOI: https://doi.org/10.17323/1609-4514-2014-14-2-367-384 (Mi mmj526) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Asymptotic properties of Arnold tongues and Josephson effect

A. Klimenkoab, O. Romaskevichcb

a Steklov Mathematical Institute of RAS
b National Research University Higher School of Economics
c École Normale Supérieure de Lyon
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DOI: https://doi.org/10.17323/1609-4514-2014-14-2-367-384
Abstract: A three-parametrical family of ODEs on a torus arises from a model of Josephson effect in a resistive case when a Josephson junction is biased by a sinusoidal microwave current. We study asymptotics of Arnold tongues of this family on the parametric plane (the third parameter is fixed) and prove that the boundaries of the tongues are asymptotically close to Bessel functions.
Key words and phrases: Arnold tongues, Josephson effect, dynamical system on the torus, rotation number.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-33020-mol-a-ved
12-01-31241-mol-a
Supported by part by RFBR grants 12-01-31241-mol-a and 12-01-33020-mol-a-ved.
Received: June 26, 2013; in revised form December 6, 2013
Bibliographic databases:
Document Type: Article
MSC: 37E45, 34E05
Language: English
Citation: A. Klimenko, O. Romaskevich, “Asymptotic properties of Arnold tongues and Josephson effect”, Mosc. Math. J., 14:2 (2014), 367–384
Citation in format AMSBIB
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\by A.~Klimenko, O.~Romaskevich
\paper Asymptotic properties of Arnold tongues and Josephson effect
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 2
\pages 367--384
\mathnet{http://mi.mathnet.ru/mmj526}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-2-367-384}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3236498}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000342789300009}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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