Charles Karney: Publication 38/85, Chirikov(1983)

B. V. Chirikov and D. L. Shepelyansky.
Statistics of Poincaré recurrences and the structure of the stochastic layer of a nonlinear resonance.
Technical Report PPPL-TRANS-133, Princeton Univ., February 1983.
20 pp. Translation of B. V. Chirikov i D. L. Shepelyanksii, Statistika Vozvratov Puankare i Struktura Stokhasticheskogo Sloya Nelineinogo Rezonansa (in Russian), Inst. Nucl. Physics Rept. INP 81–69, Novosibirsk (April 14, 1981); translated by N. M. Turitzin; edited by C. F. F. Karney.
Proc. 9th International Conf. on Nonlinear Oscillations, Kiev, USSR, Aug. 30-Sept. 6, 1981, edited by Yu. A. Mitropolsky, Vol. 2, pp. 421–424, (Naukova Dumka, Kiev 1984).
Reprint: PPPL-TRANS-133
BibTeX Entry

Motion in the stochastic layer around the separatrix of a nonlinear resonance was investigated. The integral distribution function F(τ) of trajectory recurrence times τ to the center of the layer was numerically determined. It was found that the distribution F(τ) = Aτ^−p is a power function, the exponent assuming two different values: for τ ≤ τ₀, p = 1/2 and for τ >> τ₀, p = 3/2 (time τ₀ is determined by the characteristics for the layer).