Billiards: physical and mathematical aspects. Paper from the 29th Brazilian mathematics colloquium -- 29\(^{\text o}\) Colóquio Brasileiro de Matemática, Rio de Janeiro, Brazil, July 22 -- August 2, 2013 (Q2848155)

In this book, the authors present the billiards theory. Such a theory has triggered the interest of many authors in the last few decades, and started back in 1927 in a work of \textit{G. D. Birkhoff} [Dynamical systems. New York: American Mathematical Society (1927; JFM 53.0732.01)]. This theory, although very simple to state, has presented deep results for dynamical systems and consists, naively speaking, in studying the movement of a ball in a billiard table. The results depend on the geometry of such a table, and can be regular, chaotic or even both (the latter is referred to as mixed dynamics).