Degenerate orbit flip homoclinic bifurcations with higher dimensions (Q882723)

For higher dimensional systems, bifurcations of a degenerate homoclinic orbit with orbit flip are studied. By establishing local coordinates near the homoclinic orbit, conditions are given sufficient for the existence and uniqueness of a 1-homoclinic orbit and a 1-periodic orbit. The existence of a 2-homoclinic orbit and a 2-periodic orbit is also considered. The corresponding bifurcation surfaces are given.