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Ufa Mathematical Journal, 2013, Volume 5, Issue 2, Pages 109–130
DOI: https://doi.org/10.13108/2013-5-2-109 (Mi ufa202) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Localization of Arnold tongues of discrete dynamical systems

M. G. Yumagulov

Bashkir State University, Zaki Validi str., 32, 450074, Ufa, Russia
English version PDF (1117 kB) Citations (5)
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DOI: https://doi.org/10.13108/2013-5-2-109
Abstract: The work is devoted to the exposition of the method of localizing the Arnold tongues for finite-dimensional dynamical systems with a discrete time which are the sets corresponding to rationally synchronized relations between the system's parameters. Such sets correspond to regions of parameter values for which the system has cycles of certain periods. The method allows us to obtain an approximate representation of the Arnold tongues, to study their properties in the major and minor resonances.
Keywords: bifurcation, dynamical systems, Arnold tongues, operator equations, functionalization of parameter.
Received: 26.02.2012
Russian version:
Ufimskii Matematicheskii Zhurnal, 2013, Volume 5, Issue 2, Pages 109–131
Bibliographic databases:
Document Type: Article
UDC: 517.91
MSC: 37G10, 37G15
Language: English
Original paper language: Russian
Citation: M. G. Yumagulov, “Localization of Arnold tongues of discrete dynamical systems”, Ufimsk. Mat. Zh., 5:2 (2013), 109–131; Ufa Math. J., 5:2 (2013), 109–130
Citation in format AMSBIB
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\by M.~G.~Yumagulov
\paper Localization of Arnold tongues of discrete dynamical systems
\jour Ufimsk. Mat. Zh.
\yr 2013
\vol 5
\issue 2
\pages 109--131
\mathnet{http://mi.mathnet.ru/ufa202}
\elib{https://elibrary.ru/item.asp?id=19063040}
\transl
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 2
\pages 109--130
\crossref{https://doi.org/10.13108/2013-5-2-109}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:388
    Russian version PDF:178
    English version PDF:19
    References:81
    First page:2
     
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