THE ITERATION-APPROXIMATION DECOUPLING IN THE REVERSIBLE KAM THEORY

General theorems on the persistence of quasiperiodic motions in revers ible flows and diffeomorphisms satisfying very weak nondegeneracy cond itions are obtained by a new method. The essence of this method is tha t the reversible system under consideration is embedded in a multipara meter family of reversible systems, and standard results on Diophantin e approximations of dependent quantities are then applied to Whitney-s mooth Canter foliations of invariant tori of this family. Invariant to ri are constructed for all the permissible values of m, p, q (for vect or fields V) or in, p, g, P, Q (for diffeomorphisms A) where m is the torus dimension, (q,p) is the type of the reversing involution G, and (Q,P) is the type of the involution AG. The excitation of elliptic nor mal modes is also considered. (C) 1995 American Institute of Physics.