  We apply the concept of Lagrangian descriptors to the dynamics on the
Bunimovich stadium billiard, a 2D ergodic system with singular families of
trajectories, namely, the bouncing ball and the whispering gallery orbits. They
play a central role in structuring the phase space, which is unveiled here by
means of the Lagrangian descriptors applied to the associated map on the
boundary. More interestingly, we also consider the open stadium, which in the
optical case (Fresnel's laws) can be directly related to recent microlaser
experiments. We find that the structure of the emission profile of these
systems can be easily described thanks to the open version of the Lagrangian
descriptors.
