Numerical studies on chaoticity of a classical hard-wall billiard with   openings
  Using fractal analysis, we investigate how the size of openings affects the chaotic behavior of a classical closed billiard when two openings are made on the boundary of the billiard. This kind of open billiards retains chaotic properties of original closed billiards when openings are small compared to the size of the billiard. We calculate the fractal dimension using an one-dimensional subset of all possible initial conditions that will produce trajectories of a particle injected from an opening for the billiard, and then observe how the opening size can change the classical chaotic properties of this open billiard. 
Suhan Ree