In the last three decades of the twentieth century, chaotic billiards became one of the most active and popular research areas in statistical mechanics. This started with a seminal paper by Ya. Sinai in 1970 [Si2], where he developed a mathematical apparatus for the study of hyperbolic and ergodic properties for a large class of plane billiards. He also obtained an exact formula for the entropy of billiards. Sinai's theory led to an outburst of papers in mathematics and physics journals devoted to various types of billiards on plane and space of any dimension. The remarkable progress of Sinai's theory culminated in a solution, in some form, of a classical hypothesis by L. Boltzmann (stated back in the 1880's) on the ergodicity of gases of hard balls. The advances in the study of billiards also penetrated nonequilibrium statistical mechanics and some other sciences. The goal of this book is to introduce the reader to the up-to-date theory of chaotic billiards.
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