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Averaging and integral manifolds (II)

Published online by Cambridge University Press:  17 April 2009

K. J. Palmer
K. J. Palmer
Affiliation:
Australian National University, Canberra, ACT.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 3 , June 1970 , pp. 369 - 399
Copyright
Copyright © Australian Mathematical Society 1970

References

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