This article is cited in 6 papers

On averaging in two-frequency systems with small Hamiltonian and much smaller non-Hamiltonian perturbations

A. I. Neishtadt

Space Research Institute, Russian Academy of Sciences

Abstract: A system which differs from an integrable Hamiltonian system with two degrees of freedom by a small Hamiltonian perturbation and much a smaller non-Hamiltonian perturbation is considered. The unperturbed system is isoenergetically nondegenerate. The averaging method is used for an approximate description of solutions of the exact system on a time interval inversely proportional to the amplitude of the non-Hamiltonian perturbation. The error of this description (averaged over initial conditions) is estimated from above by a value proportional to the square root of the amplitude of the Hamiltonian perturbation.

Key words and phrases: Perturbation theory, averaging method.

MSC: Primary 14P25, 57M25; Secondary 14H20, 53D99

Received: October 14, 2002; in revised form July 7, 2003

Language: English

DOI: 10.17323/1609-4514-2003-3-3-1039-1052

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