Recurrence of particles in static and time varying oval billiards

Abstract

Dynamical properties are studied for escaping particles, injected through a hole in an oval billiard. The dynamics is considered for both static and periodically moving boundaries. For the static boundary, two different decays for the recurrence time distribution were observed after exponential decay for short times: A changeover to: (i) power law or; (ii) stretched exponential. Both slower decays are due to sticky orbits trapped near KAM islands, with the stretched exponential apparently associated with a single group of large islands. For time dependent case, survival probability leads to the conclusion that sticky orbits are less evident compared with the static case.

7 pages, 6 figures, to appear in Phys Lett A

References in corpus (9)

• Hyperacceleration in a stochastic Fermi-Ulam model
• Recurrence Time Statistics for Finite Size Intervals
• Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates
• Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas
• Chaotic dynamics of the elliptical stadium billiard in the full parameter space
• Open Mushrooms: Stickiness revisited
• New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis
• Phase Space Interpretation of Exponential Fermi Acceleration
• Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries

Cited by in corpus (6)

• Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
• Escape through a time-dependent hole in the doubling map
• Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard
• Analysis of resonant population transfer in time-dependent elliptical quantum billiards
• Transition from normal to ballistic diffusion in a one-dimensional impact system
• Rotating Leaks in the Stadium Billiard