  L. Boltzmann proposed a billiard model with a planar central force problem
reflected against a line not passing through the center. He asserted that such
a system is ergodic, which thus illustrates his ergodic hypothesis. However, it
has been recently shown that when the underlying central force problem is the
Kepler problem then the system is actually integrable by Gallavotti-Jauslin.
This raises the question of whether Boltzmann's assertion holds true for some
central force problems that he considered. In this paper, we present some
geometrical and numerical analysis on the dynamics of several of these systems.
As indicated by the numerics, many of these systems show chaotic dynamics and a
system seems to be ergodic.
