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This article is cited in 70 scientific papers (total in 70 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
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.
DOI:
https://doi.org/10.4213/rm9346
 Full text:
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English version:
Russian Mathematical Surveys, 2010, 65:2, 259–318
Bibliographic databases:
     
UDC:
517.925+517.938.5
MSC: Primary 37-02; Secondary 37J05, 37J20, 37J25, 37J35, 70E40, 70E50, 70G40, 7
Received: 19.01.2010
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
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