On (h, k) manifolds with asymptotic phase

Abstract

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 admissiblehandkfunctions is also briefly analyzed. © 1997 Academic Press.