Stickiness in mushroom billiards

Details Stickiness in mushroom billiards Stickiness in mushroom billiards

2005-02-25

arxiv.org/abs/nlin/0502058v2

Chaos 15, 033105 (2005)

Nonlinear Sciences

Chaotic Dynamics

7 pages, 6 figures (corrected version with a new figure)

Scientific paper

10.1063/1.1979211

We investigate dynamical properties of chaotic trajectories in mushroom billiards. These billiards present a well-defined simple border between a single regular region and a single chaotic component. We find that the stickiness of chaotic trajectories near the border of the regular region occurs through an infinite number of marginally unstable periodic orbits. These orbits have zero measure, thus not affecting the ergodicity of the chaotic region. Notwithstanding, they govern the main dynamical properties of the system. In particular, we show that the marginally unstable periodic orbits explain the periodicity and the power-law behavior with exponent $\gamma=2$ observed in the distribution of recurrence times.

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