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On the topological structure of integrable Hamiltonian systems close to a given system. (Russian. English summary) Zbl 0926.37016
The paper is devoted to the study of the topology for the integrable perturbations of a given integrable Hamiltonian system with two degrees of freedom. The approach is based on the topological classification of integrable systems developed by Fomenko and Zieschang.
It is proved that the topological structure of the perturbed system can be obtained from the topological structure of the initial one by several steps of calculations.
Finally, the author introduces a method which may be useful for verifying whether an integrable Hamiltonian system can be approximated by integrable systems from a given class.
Reviewer: S.Zelik (Moskva)
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
70H05 Hamilton’s equations
37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
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