Bifurcation to chaotic scattering

Abstract

We investigate a novel type of bifurcation to chaos which occurs in the context of chaotic scattering. In chaotic scattering the deflection angle versus impact parameter is singular on a set of impact parameters which is fractal. This behavior is caused by the presence of a chaotic invariant set of unstable bounded orbits. In the bifurcation considered here the chaotic set arises abruptly (in a sense to be discussed) as the particle energy E decreases from above a critical value Em, to below. We call this transition an abrupt bifurcation to fully developed chaotic scattering. Numerical computation of the dimension, d, of the chaotic set shows that, in agreement with theoretical prediction, d ≈ 1/In[(Em - E)−1] near the abrupt bifurcatio