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.
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Communicated by J. N. Mather
Partially supported by NSF grant DMS 8806067
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Donnay, V.J. Using integrability to produce chaos: Billiards with positive entropy. Commun.Math. Phys. 141, 225–257 (1991). https://doi.org/10.1007/BF02101504
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DOI: https://doi.org/10.1007/BF02101504