Statistics of Poincare recurrences and the structure of the stochastic layer of a nonlinear resonance

Motion in the stochastic layer around the separatrix of a nonlinear resonance was investigated. The integral distribution function F(tau) of trajectory recurrence times tau to the center of the layer was numerically determined. It was found that the distribution F(tau) = A tau-/sup p/ is a power function, the exponent assuming two different values: for tau less than or equal to tau0, p = 1/2 and for tau >> tau0, p = 3/2 (time tau0 is determined by the characteristics of the layer)