ON DYNAMICAL SYSTEMS CLOSE TO A PRODUCT OF m ROTATIONS

Abstract

We consider one parameter families of analytic vector fields and diffeomorphisms, including for a parameter value, say epsilon = 0, the product of rotations in R-2m x R-n such that for positive values of the parameter the origin is a hyperbolic point of saddle type. We address the question of determining the limit stable invariant manifold when epsilon goes to zero as a subcenter invariant manifold when epsilon = 0.