Bifurcation to Chaotic Scattering

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 E_m, 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[(E_m - E)⁻¹] near the abrupt bifurcation.