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Linearly stable orbits in 3 dimensional billiards

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Abstract

We construct linearly stable periodic orbits in a class of billiard systems in 3 dimensional domains with boundaries containing semispheres arbitrarily far apart. It shows that the results about planar billiard systems in domains with convex boundaries which have nonvanishing Lyapunov exponents cannot be easily extended to 3 dimensions.

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Authors and Affiliations

  1. Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA

    Maciej P. Wojtkowski

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  1. Maciej P. Wojtkowski
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Communicated by J.-P. Eckmann

Supported in part by the NSF Grant DMS-8807077 and the Sloan Foundation

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Wojtkowski, M.P. Linearly stable orbits in 3 dimensional billiards. Commun.Math. Phys. 129, 319–327 (1990). https://doi.org/10.1007/BF02096985

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  • DOI: https://doi.org/10.1007/BF02096985

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