Universal Power-law Decay in Hamiltonian Systems?

Details Universal Power-law Decay in Hamiltonian Systems? Universal Power-law Decay in Hamiltonian Systems?

2002-10-16

arxiv.org/abs/nlin/0210033v1

Nonlinear Sciences

Chaotic Dynamics

Phys. Rev. Lett., in press

Scientific paper

10.1103/PhysRevLett.89.239401

The understanding of the asymptotic decay of correlations and of the distribution of Poincar\'e 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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