2017
Том 69
№ 9

All Issues

Invariant tori of locally Hamiltonian systems close to conditionally integrable systems

Loveikin Yu. V., Parasyuk I. O.

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Abstract

We study the problem of perturbations of quasiperiodic motions in the class of locally Hamiltonian systems. By using methods of the KAM-theory, we prove a theorem on the existence of invariant tori of locally Hamiltonian systems close to conditionally integrable systems. On the basis of this theorem, we investigate the bifurcation of a Cantor set of invariant tori in the case where a Liouville-integrable system is perturbed by a locally Hamiltonian vector field and, simultaneously, the symplectic structure of the phase space is deformed.

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 1, pp 70-99.

Citation Example: Loveikin Yu. V., Parasyuk I. O. Invariant tori of locally Hamiltonian systems close to conditionally integrable systems // Ukr. Mat. Zh. - 2007. - 59, № 1. - pp. 71–98.

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