Ensemble separation and stickiness influence in a driven stadium-like billiard: A Lyapunov exponents analysis

The dynamics of an ensemble of non-interacting particles suffering elastic collisions inside a driven stadium-like billiard is investigated through a four-dimensional nonlinear mapping. The system presents a resonance velocity, which plays an important role on the ensemble separation according to the initial velocities. The idea is to use the Lyapunov exponents to study the ensemble separation. We compare two different methods: (i) Finite Time Lyapunov Exponents and (ii) Wolf Linearization Algorithm. Results from both methods show good agreement regarding the separation of ensembles. Our results give support for the fact that stickiness influences the dynamics providing a crucial effect in the ensemble separation of the velocities for the time-dependent stadium-like billiard.