SMALL-ANGLE KREIN COLLISIONS IN A FAMILY OF 4-DIMENSIONAL REVERSIBLE MAPS

The small-angle Krein collision (SAKC) in four-dimensional reversible maps refers to the codimension-2 bifurcation, where the eigenvalues of the Jacobian of the map at a symmetric fixed point collide close to +1 as some relevant parameters are varied. SAKC is always associated with the bifurcation of nearby fixed points. We investigate the existence and stability of invariant curves around these fixed points for a particular family of reversible maps, and find a rich structure of the phase space.