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Invariant tori of locally Hamiltonian systems close to conditionally integrable systems

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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.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 1, pp. 71–98, January, 2007.

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Loveikin, Y.V., Parasyuk, I.O. Invariant tori of locally Hamiltonian systems close to conditionally integrable systems. Ukr Math J 59, 70–99 (2007). https://doi.org/10.1007/s11253-007-0005-4

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