Stickiness in mushroom billiards

Abstract

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.

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

References in corpus (5)

• Long-Time Correlations in the Stochastic Regime
• Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
• Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space
• Recurrence Time Statistics for Finite Size Intervals
• Effective dynamics in Hamiltonian systems with mixed phase space

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• Intrinsic stickiness in open integrable billiards: tiny border effects
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• On stable laws in a one-dimensional intermittent map equipped with a uniform invariant measure
• Chaotic properties of the truncated elliptical billiard
• Characterizing and quantifying weak chaos in fractional dynamics
• About Imperfect Mushroom Billiards