Lagrangian descriptors for the Bunimovich stadium billiard

Abstract

We apply the concept of Lagrangian descriptors to the dynamics on the Bunimovich stadium billiard, a two-dimensional 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.