ON THE ANALYSIS OF CERTAIN HIGH-DIMENSIONAL SYSTEMS WITH INNER RESONANCES

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