2005/02/28 by Eduardo G. Altmann, Adilson E. Motter, Holger Kantz +1
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #cond-mat.stat-mech #nlin.CD #quant-ph
paper · pdf · doi:10.1063/1.1979211
published as Chaos 15, 033105 (2005) · 7 pages, 6 figures (corrected version with a new figure)
arxiv created 2005/06/03 · openalex publication_date 2005/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 gamma=2 observed in the distribution of recurrence times.