Hyperbolic billiards with nearly flat focusing boundaries. I

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dc.creatorBussolari, Luca
dc.creatorLenci, Marco
dc.date2007-12-21
dc.date.accessioned2026-07-07T10:09:43Z
dc.date.available2026-07-07T10:09:43Z
dc.descriptionThe standard Wojtkowski-Markarian-Donnay-Bunimovich technique for the hyperbolicity of focusing or mixed billiards in the plane requires the diameter of a billiard table to be of the same order as the largest ray of curvature along the focusing boundary. This is due to the physical principle that is used in the proofs, the so-called defocusing mechanism of geometrical optics. In this paper we construct examples of hyperbolic billiards with a focusing boundary component of arbitrarily small curvature whose diameter is bounded by a constant independent of that curvature. Our proof employs a nonstardard cone bundle that does not solely use the familiar dispersing and defocusing mechanisms.
dc.description21 pages, 9 figures
dc.identifierhttps://arxiv.org/abs/0712.3802
dc.identifierhttp://arxiv.org/abs/0712.3802
dc.identifierPhysica D 237 (2008), no. 18, 2272-2281
dc.identifierdoi:10.1016/j.physd.2008.02.006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171404
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subject37D50; 37D25; 37A25
dc.titleHyperbolic billiards with nearly flat focusing boundaries. I
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