4TH ORDER RESONANT COLLISIONS OF MULTIPLIERS IN REVERSIBLE MAPS - PERIOD-4 ORBITS AND INVARIANT CURVES

Resonant collision of multipliers at fi of a symmetric fixed point for a 2-parameter family of 4-dimensional reversible maps is considered. Bifurcation of period-4 orbits from the fixed point and their linear s tability characteristics are briefly reviewed. In one of the three pos sible types of bifurcation (see text), a small angle secondary collisi on of the Floquet multipliers of the bifurcating periodic orbit takes place, leading to the bifurcation of invariant curves from the orbit. The invariant curves are calculated in a perturbation scheme in the le ading order of perturbation, The secondary bifurcation is found to be of superthreshold type. An interesting pattern in the vicinity of the resonant collision, involving families of invariant curves and 2-tori, emerges. Results of numerical iterations, corroborating the picture c onjectured on the basis of perturbation calculations, are presented. C orresponding results on resonant collisions at -1 are briefly stated.