This research project investigated the phase-space dynamics of a new geometrical configuration comprised of circular outer and inner bumpers. Several computer simulations were developed to investigate the behavior that the phase space exhibits as a function of two system parameters, the size of the inner bumper and the position of its center. Depending upon the inital conditions, the system exhibited a combination of stable, predictable, nonchaotic orbits and unstable, chaotic orbits. The structures that formed as a result of different combinations of orbits were classified into five regions. The transitions between these regions, the structure within these regions, and the stability of these regions were studied in-depth. In the study of the structure, most of the regions that were found were self-similar and, therefore, fractal in nature.