Abstract
We investigate the 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 γ=2 observed in the distribution of recurrence times.
Original language | English (US) |
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Article number | 033105 |
Journal | Chaos |
Volume | 15 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2005 |
Funding
E.G.A. is supported by CAPES (Brazil) and DAAD (Germany). A.E.M. is supported by the U.S. Department of Energy under Contract No. W-7405-ENG-36.
ASJC Scopus subject areas
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
- Mathematical Physics