Conditions of stochasticity of two-dimensional billiards

There are two known mechanisms that produce chaos in billiard systems. The first one, discovered by Ya. G. Sinai, is called dispersing, the second, found by the author, is called defocusing. The same mechanisms produce chaos for geodesic flows. Some results on two-dimensional billiards, which indicate that only these two mechanisms can produce chaos in Hamiltonian systems, are discussed.