Dynamics of classical quadrupole moment II

A number of problems in dynamical physics can be reduced to the study of an area-preserving map a plane onto itself. We investigate the problem whose dynamics leads to an area-preserving map a sphere onto itself. The main benefit of the symmetry of the map is that this system may have homoclinic points lying on curves that divide the unit sphere. The existence of solutions that are either ordered or chaotic depends sensitively on both the parameters of the problem, and on the initial conditions. We study numerically the behavior, as a parameter is varied, of orbits of the reversible area-preserving map.