Complementing the work of Alhassid et al. we study the global dynamics of the averaged system of the generalized van der Waals interaction in the reduced space which is a two-dimensional sphere. We find lines of local ‘‘pitchfork’’ and global ‘‘oyster’’ bifurcations emerging from the known integrable cases β=1/2, 1, 2; this explains the chaos-order-chaos transition. We present the libration and circulation modes of the Runge-Lenz vector and its stability domains. The appearance-disappearance pattern of separatrices for the known integrable cases leads us to conjecture that those are the only ones.

• Received 2 November 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.985