The open unsymmetrical stadium billiard

In open billiards a particle can escape from the cavity through a leak. This type of systems have received special attention because of their applications to a wide variety of physical phenomena ranging from hydrodynamics to quantum chaos and astronomy. Chaotic leaked billiards are characterized by a so called transient behavior, i.e. by the presence of chaotic motion with a finite life time impossible to be studied just through the analysis of its asymptotic behavior. Under this scenario, we consider the quarter stadium billiard to study the influence of leaking marginal unstable periodic orbits. A rigorous statistical analysis of the survival probability is presented, setting up the classical trajectories' solution in such a way that the system only depends on its partial separability and construct the Birkhoff map. The possibility of more than one leak into a billiard is also considered.