  We present an analytical description of the distribution of diagonal lines in
Recurrence Plots (RPs) for white noise and chaotic systems, and find that the
latter one is linked to the correlation entropy. Further we identify two
scaling regions in the distribution of diagonals for oscillatory chaotic
systems that are hinged to two prediction horizons and to the geometry of the
attractor. These scaling regions cannot be observed with the
Grassberger-Procaccia algorithm. Finally, we propose methods to estimate
dynamical invariants from RPs.
