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

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).