Arnold's theorem on properly degenerate systems with the Rüssmann nondegeneracy

摘要

In this paper, we investigate the persistence of invariant tori for the nearly integrable Hamiltonian system H(x, y) =h(y) + εp((x), y) + ε2Q(x, (y)), whereh(y) and εp((x), y)the order of the parameter ε in the perturbation ε2Q(x,y) is not enough and that the measure estimate involves in parts of frequencies with small parameter.