REDUCTIONS, RELATIVE EQUILIBRIA, AND BIFURCATIONS IN THE GENERALIZED VAN-DER-WAALS POTENTIAL - RELATION TO THE INTEGRABLE CASES

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