Degenerate Dynamical Systems and the Disappearance of (K.A.M.-Type) Integrals of Motion

ABSTRACT The problem of constructing the stochasticity criterion of a degenerate near-integrable dynamical system is considered. We show that in certain cases the above criterion can be found as the limit of the corresponding stochasticity criteria of a family of non-degenerate systems, whose limit is the degenerate one.