Escape probability for classically chaotic systems

A statistical approach to study the escape of an ensemble of particles from classical chaotic systems is proposed. The universal kinetic decay laws, exponential and algebraic, are found through the velocity angle distribution and shown to be specific of distinct motion regimes in the billiards with a small opening. On the basis of the particular case of the dispersing Sinai billiard the escape probability is given in explicit form and the temporal and geometrical conditions are enunciated to make controlled observations of decay dynamics in numerical experiments.