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.
KeywordsEntropy Microwave Stein Dinates Suffix
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