Averaging and integral manifolds (II)

Abstract

In the first part of this paper (written jointly with W.A. Coppel) the existence and properties of an integral manifold were established for the systemx′ = f(t, x, y)y′ = A(t)y + g(t, x, y)where f and g are “integrally small”. In this second part of the paper the stability properties of the integral manifold are investigated. Solutions are found which are bounded on the positive half of the real line and it is shown that these solutions approach the manifold exponentially and, moreover, that they are asymptotic to particular solutions on the manifold.