Excitation of elliptic normal modes of invariant tori in volume preserving flows (Q2770246)

Given a codimension-two \(n\)-dimensional invariant torus with a quasiperiodic motion of a volume preserving real-analytic dynamical system, consider a perturbation of the system, i.e. a real-analytic family of divergent-free vector fields depending of the perturbation parameter \(\mu\). Assume that the initial torus is invariant under all perturbed systems, carries quasiperiodic motions with rationally independent frequencies and for all perturbations the eigenvalues of the variational matrices are purely imaginary. The author proves that for such perturbations which are sufficiently small in the real analytic topology there exists a quasiperiodic invariant \((n+1)\) tori which fill a positive Lebesgue measure set in the product of the phase space with the \(\mu\)-parameter space.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00062].