Chaotic scattering modelled by an inclined billiard (Q1118227)

Chaotic scattering, as observed in satellite encounters and in other problems, is modelled by a simple billiard: a point particle bounces on two disks and in addition is subjected to a constant acceleration. In an appropriate limit, this problem reduces to a piecewise linear mapping. We consider a one-parameter family of orbits obtained by starting the particle at rest from a constant height. We find that this family exhibits chaotic scattering: it has an infinite number of discontinuities, forming a self-similar Cantor set. With the help of symbolic dynamics, the structure of the family can be completely elucidated.