Journal
RUSSIAN MATHEMATICAL SURVEYS
Volume 65, Issue 2, Pages 259-317Publisher
TURPION LTD
DOI: 10.1070/RM2010v065n02ABEH004672
Keywords
topology; stability; periodic trajectory; critical set; bifurcation set; bifurcation diagram
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Funding
- Federal Target Programme Scientific and Scientific-Pedagogical Staff of Innovative Russia [2009-1.5-503-004-019]
- Leading Scientific Schools [HIII-660.2008.1]
- Russian Federation for Support of Young Doctors of the Sciences [MII-5239.2008.1]
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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.
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