Hans Jurgen Korsch and Frank Zimmer

Niveau: Supérieur, Licence, Bac+3
Chaotic Billiards Hans Jurgen Korsch and Frank Zimmer Fachbereich Physik, Univ. Kaiserslautern, D-67653 Kaiserslautern, Germany Abstract. 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 shows an intricate mixture of regular and irregular behavior. Irregular orbits are characterized by an extremely sensitivity with respect to the initial conditions. Such billiard systems are exemplarily suited for educational purposes as models for simple systems with complicated dynamics as well as for far-reaching fundamental investigations. 1 Introduction In the past decades, classical physics has witnessed an unexpected, impetuous development, which has led to an entirely new understanding of the classical dynamics of simple systems, an area in physics that has usually been presumed to be generally understood and concluded. It became evident, however, that { contrary to the concepts conveyed by most physics textbooks { even simplest, completely deterministic systems may show irregular, chaotic behavior, that is as unpredictable as the tossing of a coin. Commonly one accepted a random, stochastic behavior only for a system with a large ( 10 23 ) number of degrees of freedom, e.

• gram billiard


• called irregular


• can easily


• billiard systems


• such


• irregular behavior


• show instabilities


• few examples