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JOURNALS // Regular and Chaotic Dynamics // Archive

Regul. Chaotic Dyn., 1997 Volume 2, Issue 2, Pages 98–105 (Mi rcd990)

On the Topological Structure of the Integrable Hamiltonian Systems Closed to the Given

V. V. Kalashnikov

119899, Russia, Moscow, Vorobyovy Gory, Moscow State University, Faculty of Mechanics and Mathematics, Department of Differential Geometry

Abstract: Well known KAM theory describes the behaviour of the hamiltonian systems closed to the integrable one. In this paper we investigate the topology of integrable systems with two degrees of freedom near to some known integrable system. We say that two integrable systems are closed to each other, if the correspondent hamiltonians are closed. We will show that the topological structure of the perturbed integrable system can be obtained from the topological structure of the unperturbed system by means of several steps of calculations.
As a result of our research we introduce a method which helps to solve the problem whether an integrable hamiltonian system can be approximated by a given family of integrable systems.

Received: 10.12.1996

DOI: 10.1070/RD1997v002n02ABEH000041



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