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Chaos pp 45–66Cite as

Billiard Systems

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Abstract

An extremely simple example for demonstrating chaotic dynamics in conservative systems numerically is that of Birkhoff’s billiard [3.1], i.e. the frictionless motion of a particle on a plane billiard table bounded by a closed curve [3.2]–[3.7]. The limiting cases of strictly regular (integrable) and strictly irregular (ergodic’ or ‘mixed’) systems can be illustrated, as well as the typical case, which shows a complicated mixture of regular and irregular behavior. The onset of chaos follows the so-called Poincaré scenario, i.e. the consecutive destruction of invariant tori for increasing deviation from integrability as described by the KAM-theory and the Poincaré-Birkhoff theorem discussed in Chap. 2.

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Authors and Affiliations

  1. Fachbereich Physik, Universität Kaiserslautern, Erwin-Schrödinger-Strasse, D-67663, Kaiserslautern, Germany

    Professor Dr. H. J. Korsch & Professor Dr. H.-J. Jodl

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  1. Professor Dr. H. J. Korsch
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  2. Professor Dr. H.-J. Jodl
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© 1999 Springer-Verlag Berlin Heidelberg

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Korsch, H.J., Jodl, HJ. (1999). Billiard Systems. In: Chaos. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03866-6_3

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  • DOI: https://doi.org/10.1007/978-3-662-03866-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03868-0

  • Online ISBN: 978-3-662-03866-6

  • eBook Packages: Springer Book Archive

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