Perturbations of Lower Dimensional Tori in the Resonant Zone for Reversible Systems

Consider a nearly integrable system which is reversible with respect to an involution ofŽn, n.type. For a given l-resonant surface, 1 l n, we show that there is a subset of it with positive measure, such that in each resonant torus corresponding to a point of this set, at least one dimensional invariant submanifold can survive any small perturbations