Surviving lower-dimensional tori of an invariant resonant torus with any number of resonances
Frank Trujillo · Transactions of the American Mathematical Society · 2024
We provide sufficient conditions on a class of analytic non-convex integrable Hamiltonians that guarantee the existence, in any sufficiently small analytic perturbation, of at least one invariant lower-dimensional torus associated with an invariant resonant torus of the unperturbed Hamiltonian. This criterion does not impose any restriction on the number of resonances of the resonant torus and, to our knowledge, provides the first persistence result for lower-dimensional tori of any codimension associated with a resonant torus, dealing with arbitrary, sufficiently small perturbations of an integrable system.