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Apparent fractal dimensions in the HMF model

L. Sguanci·D. H. E. Gross·S. Ruffo
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Abstract

We show that recent observations of fractal dimensions in the $μ$-space of $N$-body Hamiltonian systems with long-range interactions are due to finite $N$ and finite resolution effects. We provide strong numerical evidence that, in the continuum (Vlasov) limit, a set which initially is not a fractal (e.g. a line in 2D) remains such for all finite times. We perform this analysis for the Hamiltonian Mean Field (HMF) model, which describes the motion of a system of $N$ fully coupled rotors. The analysis can be indirectly confirmed by studying the evolution of a large set of initial points for the Chirikov standard map.

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L. Sguanci, D. H. E. Gross, S. Ruffo. 2004-07-14. Apparent fractal dimensions in the HMF model. https://doi.org/10.1080/00411450500274766

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