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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
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
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
Linking options:
https://www.mathnet.ru/eng/rm9346https://doi.org/10.1070/RM2010v065n02ABEH004672 https://www.mathnet.ru/eng/rm/v65/i2/p71
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Abstract page: | 1593 | Russian version PDF: | 595 | English version PDF: | 55 | References: | 152 | First page: | 58 |
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