Chaos pp 45-66 | Cite as

Billiard Systems

  • H. J. Korsch
  • H.-J. Jodl


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.


Phase Space Periodic Orbit Boundary Curve Invariant Torus Regular Orbit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • H. J. Korsch
    • 1
  • H.-J. Jodl
    • 1
  1. 1.Fachbereich PhysikUniversität KaiserslauternKaiserslauternGermany

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