Escape time statistics for mushroom billiards

Abstract

Chaotic orbits of mushroom billiards display intermittent behaviors. We investigate statistical properties of this system by constructing an infinite partition on the chaotic part of a Poincaré surface which illustrates details of chaotic dynamics. Each piece of the infinite partition has an unique escape time from the half disk region, and from this result it is shown that, for fixed values of the system parameters, the escape time distribution obeys power law $1/t_{\mathrm{esc}}^3$.

7 pages, 8 figures

References in corpus (5)

• Long-Time Correlations in the Stochastic Regime
• Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
• Stickiness in mushroom billiards
• Periodic orbit theory of strongly anomalous transport
• Nonperiodic echoes from mushroom billiard hats

Cited by in corpus (5)

• Leaking Chaotic Systems
• Nonperiodic echoes from quantum mushroom billiard hats
• On stable laws in a one-dimensional intermittent map equipped with a uniform invariant measure
• $1/f$ Spectrum and 1-Stable Law in One-Dimensional Intermittent Map with Uniform Invariant Measure and Nekhoroshev Stability
• Homogeneous Connectivity of Potential Energy Network in a Solidlike State of Water Cluster