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Russian Mathematical Surveys, 2010, Volume 65, Issue 2, Pages 259–318
DOI: https://doi.org/10.1070/RM2010v065n02ABEH004672 (Mi rm9346) 		 
This article is cited in 105 scientific papers (total in 106 papers)

Topology and stability of integrable systems

A. V. Bolsinovab, A. V. Borisovc, I. S. Mamaevc

a M. V. Lomonosov Moscow State University
b School of Mathematics, Loughborough University, UK
c Institute of Computer Science, Izhevsk
English version PDF (1302 kB) Citations (106)
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DOI: https://doi.org/10.1070/RM2010v065n02ABEH004672
Abstract: In this paper a general topological approach is proposed for the study of stability of periodic solutions of integrable dynamical systems with two degrees of freedom. The methods developed are illustrated by examples of several integrable problems related to the classical Euler–Poisson equations, the motion of a rigid body in a fluid, and the dynamics of gaseous expanding ellipsoids. These topological methods also enable one to find non-degenerate periodic solutions of integrable systems, which is especially topical in those cases where no general solution (for example, by separation of variables) is known.
Bibliography: 82 titles.
Keywords: topology, stability, periodic trajectory, critical set, bifurcation set, bifurcation diagram.
Received: 19.01.2010
Russian version:
Uspekhi Matematicheskikh Nauk, 2010, Volume 65, Issue 2(392), Pages 71–132
DOI: https://doi.org/10.4213/rm9346
Bibliographic databases:
Document Type: Article
UDC: 517.925+517.938.5
MSC: Primary 37-02; Secondary 37J05, 37J20, 37J25, 37J35, 70E40, 70E50, 70G40, 7
Language: English
Original paper language: Russian
Citation: A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and stability of integrable systems”, Uspekhi Mat. Nauk, 65:2(392) (2010), 71–132; Russian Math. Surveys, 65:2 (2010), 259–318
Citation in format AMSBIB
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    Remarks
    This publication is cited in the following 106 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
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    Abstract page:1593
    Russian version PDF:595
    English version PDF:55
    References:152
    First page:58
     
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