  We apply a molecular dynamics scheme to analyze classically chaotic
properties of a two-dimensional circular billiard system containing two
Coulomb-interacting electrons. As such, the system resembles a prototype model
for a semiconductor quantum dot. The interaction strength is varied from the
noninteracting limit with zero potential energy up to the strongly interacting
regime where the relative kinetic energy approaches zero. At weak interactions
the bouncing maps show jumps between quasi-regular orbits. In the
strong-interaction limit we find an analytic expression for the bouncing map.
Its validity in the general case is assessed by comparison with our numerical
data. To obtain a more quantitative view on the dynamics as the interaction
strength is varied, we compute and analyze the escape rates of the system.
Apart from very weak or strong interactions, the escape rates show consistently
exponential behavior, thus suggesting strongly chaotic dynamics and a phase
space without significant sticky regions within the considered time scales.
