Tanaka Hiroyuki, Shudo Akira
Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 2):036211. doi: 10.1103/PhysRevE.74.036211. Epub 2006 Sep 26.
The recurrence time distribution of mushroom billiards with a parabolic-shaped hat is investigated. Classical dynamics exhibits sharply divided phase space, and the recurrence time distribution obeys the algebraic law like well-known classes of billiards. However, due to the existence of a specific type of marginally unstable periodic orbits that forms a crossing in phase space, the sticky motion occurs not as a simple drift along the straight line. Numerical experiments reveal and also theoretical analyses predict that an exponent for the cumulative recurrence time distribution approaches 2 in the asymptotic regime, but in a relatively small recurrence time scale it significantly deviates from the predicted universality, which is explained by the slowdown behavior around a crossing point of the periodic orbit family.
