On invariant tori with prescribed frequency in Hamiltonian systems (Q329869)

This paper studies the persistence of invariant tori for analytic nearly integrable Hamiltonian systems with prescribed frequency under the Bryuno-Rüssmann non-resonant condition, when the Kolmogorov non-degeneracy condition is violated. By introducing external parameters and rational approximations, they proved that if the Brouwer topological degree of the frequency mapping is nonzero at some Bryuno-Rüssmann frequency, then the invariant torus with this frequency persists under small perturbation.