Routes to chaotic scattering

Abstract

The onset of chaotic behavior in a class of classical scattering problems is shown to occur in two possible ways. One is abrupt and is related to a change in the topology of the energy surface. The other arises as a result of a complex sequence of saddle-node and period doubling bifurcations. The abrupt bifurcation represents a new generic route to chaos and yields a characteristic scaling of the frac- tal dimension associated with the scattering function as [ln(${E}_{c}$-E${)}^{\mathrm{\ensuremath{-}}1}$${]}^{\mathrm{\ensuremath{-}}1}$, for particle energies E near the critical value ${E}_{c}$ at which the scattering becomes chaotic.