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 γ=2 observed in the
distribution of recurrence times.Comment: 7 pages, 6 figures (corrected version with a new figure