Initial-value space structure in irregular gravitational scattering

Gravitational scattering of a single star by a stellar pair, in an initially circular orbit, is investigated numerically through the generation of initial-value space images showing final characteristics of the system versus initial values. This space is composed of regions for which simple deflection or exchange occurs after a single close approach between the star and the pair, and, separating these regions, a network of resonance ``rivers,'' for which the three stars become temporarily mutually bound, exhibiting complicated, chaotic behavior before one particle is eventually ejected. We discuss the general features of the initial-value space, with emphasis on the resonance regions, which are found to contain small-scale, bandlike structure, and explain the origin of this structure with a straightforward dynamical argument. An expression for the scaling of the bands is derived. High-resolution one-dimensional slices are taken through the initial-value space images, which indicate that the small-scale structure can be considered to be continuous in one direction and discontinuous in the transverse direction. Similarities with standard chaotic scattering systems are discussed. Finally, we relate the locations of the resonance regions to geometrical degeneracies in the positions of the three stars at close approach.