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. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY -NC license (http:// creativecommons .org /licenses /by -nc /4 .0/).
Billiards in generic convex bodies have positive topological entropy
Del Magno G.;
2024-01-01
Abstract
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. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY -NC license (http:// creativecommons .org /licenses /by -nc /4 .0/).File in questo prodotto:
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