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Hypothesis of strong chaos and anomalous diffusion in coupled symplectic maps

Eduardo G. Altmann·Holger Kantz
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Abstract

We investigate the high dimensional Hamiltonian chaotic dynamics in $N$ coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random walk {\em inside} the area corresponding to regular islands of the uncoupled maps. As a consequence, we observe long intermediate regimes of power-law decay of the recurrence time statistics (with exponent $γ=0.5$) and of ballistic motion. The asymptotic decay of correlations and anomalous diffusion depend on the stickiness of the $N$-dimensional invariant tori. Detailed numerical simulations show weaker stickiness for increasing $N$ suggesting that high-dimensional Hamiltonian systems asymptotically fulfill the demands of the usual hypotheses of strong chaos.

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Eduardo G. Altmann, Holger Kantz. 2007-03-23. Hypothesis of strong chaos and anomalous diffusion in coupled symplectic maps. https://doi.org/10.1209/0295-5075%2F78%2F10008

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