Billiards in generic convex bodies have positive topological entropy

Bessa, Mário; Del Magno, Gianluigi; Dias, João Lopes; Gaivão, José Pedro; Torres, Maria Joana

http://hdl.handle.net/10400.2/16743

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We show that there exists a C2-open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits.