摘要：Billiards, having wide connections with statistical physics and geometry, constitute a class of dynamical systems with singularities. This talk will briefly survey the most important facts and results in billiards (especially the chaotic billiards) and the Pesin theory of smooth maps with singularities. We will give a sketch of proof of a criterion about ergodic homoclinic class applicable for billiards, which could allow us to establish ergodicity and nonuniform hyperbolicity.
