Bifurcation of coisotropic invariant tori under locally Hamiltonian perturbations of integrable systems and nondegenerate deformation of symplectic structure

We study the bifurcation problem for a Cantor set of coisotropic invariant tori in the case where a Liouville-integrable Hamiltonian system undergoes locally Hamiltonian perturbations and, simultaneously, a deformation of the symplectic structure of the phase space. We consider a new case where the deformed symplectic structure generates a nondegenerate matrix of the Poisson brackets of action variables. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 221–232, April–June, 2006.