On the analysis of certain high dimensional systems with inner resonances

Abstract

In this paper, the normal forms and the related coefficients, of high dimensional inner resonant systems, are explored. Using a recently developed approach, calculations of normal forms (especially the related coefficients) are much easier, compared to the existing methods. A general four dimensional system with two pairs of pure imaginary eigenvalues is used as an example, and normal forms in resonant model p:q are determined. The coefficients of normal forms related to different possible resonant models; namely, 1:2, 1:3, 1:4, 2:1, 3:1 and 4:1, are considered. The theory presented here can be applied to other higher order inner resonant cases as well. (C) 1998 Academic Press Limited.