Using integrability to produce chaos: Billiards with positive entropy |
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Authors: | Victor J Donnay |
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Institution: | (1) Department of Mathematics, Bryn Mawr College, 19010 Bryn Mawr, PA, USA |
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Abstract: | A new open class of convex 2 dimensional planar billiards with positive Lyapunov exponent almost everywhere is constructed. We introduce the notion of a focusing arc and show that such arcs can be used to build billiard systems with positive Lyapunov exponents. We prove that under smallC
6 perturbations, focusing arcs remain focusing and thereby show that perturbations of the Bunimovich stadium billiard have positive Lyapunov exponents.Partially supported by NSF grant DMS 8806067 |
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