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Uspekhi Mat. Nauk, 2010, Volume 65, Issue 2(392), Pages 71–132 (Mi umn9346)  

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: PDF file (1586 kB)
References: PDF file   HTML file

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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    This publication is cited in the following articles:
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    5. T. B. Ivanova, “Postroenie bifurkatsionnoi diagrammy i analiz ustoichivosti zhidkogo samogravitiruyuschego ellipticheskogo tsilindra s vnutrennim vrascheniem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 4, 77–86  mathnet  elib
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