Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase
  Space   The phase space of a typical Hamiltonian system contains both chaotic and
regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon
is the algebraic decay of correlations and recurrence time distributions. For
area-preserving maps, this has been attributed to the stickiness of boundary
circles, which separate chaotic and regular components. Though such dynamics
has been extensively studied, a full understanding depends on many fine details
that typically are beyond experimental and numerical resolution. This calls for
a statistical approach, the subject of the present work. We calculate the
statistics of the boundary circle winding numbers, contrasting the distribution
of the elements of their continued fractions to that for uniformly selected
irrationals. Since phase space transport is of great interest for dynamics, we
compute the distributions of fluxes through island chains. Analytical fits show
that the "level" and "class" distributions are distinct, and evidence for their
universality is given.

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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an