2019
Том 71
№ 9

All Issues

Loveikin Yu. V.

Articles: 1
Article (Ukrainian)

Invariant tori of locally Hamiltonian systems close to conditionally integrable systems

Loveikin Yu. V., Parasyuk I. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 1. - pp. 71–98

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.