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Universal Power-law Decay in Hamiltonian Systems?

M. Weiss·L. Hufnagel·R. Ketzmerick
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Abstract

The understanding of the asymptotic decay of correlations and of the distribution of Poincaré recurrence times $P(t)$ has been a major challenge in the field of Hamiltonian chaos for more than two decades. In a recent Letter, Chirikov and Shepelyansky claimed the universal decay $P(t) \sim t^{-3}$ for Hamiltonian systems. Their reasoning is based on renormalization arguments and numerical findings for the sticking of chaotic trajectories near a critical golden torus in the standard map. We performed extensive numerics and find clear deviations from the predicted asymptotic exponent of the decay of $P(t)$. We thereby demonstrate that even in the supposedly simple case, when a critical golden torus is present, the fundamental question of asymptotic statistics in Hamiltonian systems remains unsolved.

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M. Weiss, L. Hufnagel, R. Ketzmerick. 2002-10-16. Universal Power-law Decay in Hamiltonian Systems?. https://doi.org/10.1103/physrevlett.89.239401

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