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How High-Dimensional Stadia Look Like

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Abstract:

We give the affirmative answer to the long-standing question whether or not the mechanism of defocusing can produce a chaotic behavior in high-dimensional Hamiltonian systems. To do this we prove that billiards in a class of regions in R n, n>2, with focusing and flat boundary components have nonvanishing Lyapunov exponents.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA, , , , , , US

    Leonid A. Bunimovich

  2. Center for Nonlinear Systems, MS B-258, Los Alamos National Laboratory, Los Alamos, NM 87545, USA, , , , , , US

    Jan Rehacek

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  1. Leonid A. Bunimovich
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  2. Jan Rehacek
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Received: 1 June 1997 / Accepted: 3 March 1998

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Bunimovich, L., Rehacek, J. How High-Dimensional Stadia Look Like. Comm Math Phys 197, 277–301 (1998). https://doi.org/10.1007/s002200050451

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  • DOI: https://doi.org/10.1007/s002200050451

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