Abrupt bifurcation to chaotic scattering with discontinuous change in fractal dimension.

Abstract

One of the major routes to chaotic scattering is through an abrupt bifurcation by which a nonattracting chaotic saddle is created as a system parameter changes through a critical value. In a previously investigated case, however, the fractal dimension of the set of singularities in the scattering function changes continuously through the bifurcation. We describe a type of abrupt bifurcation to chaotic scattering where this physically relevant dimension changes discontinuously at the bifurcation. The bifurcation is illustrated using a class of open Hamiltonian systems consisting of Morse potential hills.