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Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space

B. V. Chirikov·D. L. Shepelyansky
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Abstract

By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincaré recurrences P(τ) and correlations C(τ) asymptotically decay in time as P ~ C/τ~ 1/τ^3. It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent p=3 should be also valid for a general chaos border.

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B. V. Chirikov, D. L. Shepelyansky. 1998-07-28. Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space. https://doi.org/10.1103/physrevlett.82.528

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