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The K-property of “orthogonal” cylindric billiards

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Abstract

Toric billiards with cylindric scatterers (briefly cylindric billards) generalize the class of Hamiltonian systems of elastic hard balls. In this paper a class of cylindric billiards is considered where the cylinders are “orthogonal” or more exactly: the constituent space of any cylindric scatterer is spanned by some of the (of course, orthogonal) coordinate vectors adapted to the euclidean torus. It is shown that the natural necessary condition for the K-property of such billiards is also sufficient.

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Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364, Budapest, Hungary

    Domokos Szász

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  1. Domokos Szász
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Communicated by Ya. G. Sinai

Research supported by the Hungarian National Foundation for Scientific Research, grant No. 1902

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Szász, D. The K-property of “orthogonal” cylindric billiards. Commun.Math. Phys. 160, 581–597 (1994). https://doi.org/10.1007/BF02173431

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  • DOI: https://doi.org/10.1007/BF02173431

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