HOMOCLINIC BIFURCATIONS OF PLANE MOTION IN GENERAL CUBIC POTENTIALS

An analytic study of horseshoe chaos in a plane conservative system wi th a cubic potential is presented. It is shown that this problem with two degrees of freedom can be reduced to a time-periodically perturbed Hamiltonian system with just one degree of freedom. The unperturbed r educed system exhibits homoclinic paths, and the main goal of our stud y is the investigation of their break-up. The determination of the Mel nikov function shows that there is no contribution from two of the fou r cubic potential terms. The locus of homoclinic bifurcation in a para meter plane is computed and this bifurcation can be interpreted in ter ms of energy arguments. It was found that an increase of the total ene rgy leads - independent of the particular parameter combination - from non-chaotic to chaotic motion.