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Sbornik: Mathematics, 2013, Volume 204, Issue 1, Pages 114–132
DOI: https://doi.org/10.1070/SM2013v204n01ABEH004293 (Mi sm7928) 		 
This article is cited in 27 scientific papers (total in 27 papers)

The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems

I. N. Sergeev

Faculty of Mechanics and Mathematics, Moscow State University
English version PDF (346 kB) Citations (27)
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DOI: https://doi.org/10.1070/SM2013v204n01ABEH004293
Abstract: Lyapunov-type oscillation and wandering indicators are defined for solutions of systems of differential equations; these are the average frequency of zeros for the projection of a solution onto some line and the average angular velocity of rotation of a solution about the origin in some basis, respectively. An integral equality relating these indicators is obtained. The indicators introduced are shown to coincide if, prior to averaging, the oscillation indicators are minimized over all possible lines, and the wandering indicators over all possible bases.
Bibliography: 17 titles.
Keywords: differential system, zeros of solutions, oscillation and wandering, characteristic exponents.
Received: 02.09.2011 and 06.11.2012
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 1, Pages 119–138
DOI: https://doi.org/10.4213/sm7928
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: 34C10
Language: English
Original paper language: Russian
Citation: I. N. Sergeev, “The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems”, Mat. Sb., 204:1 (2013), 119–138; Sb. Math., 204:1 (2013), 114–132
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v204/i1/p119
    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:772
    Russian version PDF:234
    English version PDF:14
    References:103
    First page:34
     
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