Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Apparent fractal dimensions in the HMF model   We show that recent observations of fractal dimensions in the $\mu$-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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The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin