Universal Power-law Decay in Hamiltonian Systems?

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.

arXiv commentPhys. Rev. Lett., in press

References in corpus (1)

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

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