Absolute Focusing and Ergodicity of Billiards

    2003, Volume 8, Number 1, pp.  15-28

    Author(s): Bunimovich L. A.

    We show that absolute focusing is a necessary condition for a focusing component to be a part of the boundary of a hyperbolic billiard. A sketch of the proof of a general theorem on hyperbolicity and ergodicity of two-dimensional billiards with all three (focusing, dispersing and neutral) components of the boundary is given. The example of a simply connected domain (container) is given, where a system of $N$ elastically colliding balls is ergodic for any $1 \leqslant N <\infty$.
    Citation: Bunimovich L. A., Absolute Focusing and Ergodicity of Billiards, Regular and Chaotic Dynamics, 2003, Volume 8, Number 1, pp. 15-28

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