a1 Australian National University, Canberra, ACT.
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 system
x′ = 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.
(Received February 23 1970)