International Journal of Mathematics and Mathematical Sciences 
Volume 7 (1984), Issue 4, Pages 625-661
doi:10.1155/S0161171284000685

Invariant manifolds and alternative approaches to reductive perturbation theory: dissipative systems

Hedley C. Morris,1,3 Derek Sheil,2 and Roger Dodd2

 1Department of Mathematics, Claremont Graduate School, Claremont 91711, California, USA
2Trinity College Dublin, Ireland
3School of Mathematics, Trinity College Dublin, Ireland
Received 19 June 1984

Abstract

This paper is concerned with the limiting process known as Reductive Perturbation Theory. A new view of both conventional reductive perturbation theory and the higher order theory of Kodama is presented for a general class of dissipative systems. An alternative Iterative approach to the determination of higher order corrections is outlined.