On h, k.Manifolds with Asymptotic Phase*

We introduce the notion of h, k.manifolds and give conditions under which the property of being a manifold with asymptotic phase holds. These conditions allow the construction of a transformation of the variational equation of a nonlinear nonautonomous systems with h, k.dichotomies, into an almost decoupled quasilinear system. The class of admissible h and k functions is also briefly analyzed. Q 1997 Academic Press