Summary
The frictionless motion of a particle on a plane billiard table bounded by a closed curve provides a very simple example of a conservative classical system with non-trivial, chaotic dynamics. The limiting cases of strictly regular (‘integrable’) and strictly irregular (‘ergodic’) systems can be illustrated, as well as the typical case, which displays an intricate mixture of regular and irregular behavior. Irregular orbits are characterized by an extreme sensitivity to initial conditions. Such billiard systems are extremely well suited for educational purposes as models of simple systems with complicated dynamics, as well as for far-reaching fundamental investigations.
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Korsch, H.J., Zimmer, F. (2002). Chaotic Billiards. In: Computational Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04804-7_2
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