Soft chaos in a Hamiltonian system with step potential. II. Topological properties

In this series of papers the stochastic and topological properties of the relative motion of three particles on the line which interact through piecewise constant pair potentials (hard-core repulsion, short-range attraction, and long-range confinement) are examined. In part II we analyze the topology of the ergodic components in the lowest energy range E (−2, −1/2). The ergodic components are shown to be homeomorphic to connected sums of tori. Their number starts with two at the lowest energies; as the energy tends to −1/2 it becomes asymptotically proportional to the number of different momenta. Hence the genus of the ergodic components may be interpreted as measure of the chaoticity of the system for E (−2, −1/2).