Invariant tori of locally Hamiltonian systems close to conditionally integrable systems
AbstractWe 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.
How to Cite
LoveikinY. V., and ParasyukI. O. “Invariant Tori of Locally Hamiltonian Systems Close to Conditionally Integrable Systems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 1, Jan. 2007, pp. 71–98, http://umj.imath.kiev.ua/index.php/umj/article/view/3292.