Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Resonance Overlap and Hill Stability Criteria Revisited   We review the orbital stability of the planar circular restricted three-body
problem, in the case of massless particles initially located between both
massive bodies. We present new estimates of the resonance overlap criterion and
the Hill stability limit, and compare their predictions with detailed dynamical
maps constructed with N-body simulations. We show that the boundary between
(Hill) stable and unstable orbits is not smooth but characterized by a rich
structure generated by the superposition of different mean-motion resonances
which does not allow for a simple global expression for stability.
  We propose that, for a given perturbing mass $m_1$ and initial eccentricity
$e$, there are actually two critical values of the semimajor axis. All values
$a < a_{\rm Hill}$ are Hill-stable, while all values $a > a_{\rm unstable}$ are
unstable in the Hill sense. The first limit is given by the Hill-stability
criterion and is a function of the eccentricity. The second limit is virtually
insensitive to the initial eccentricity, and closely resembles a new resonance
overlap condition (for circular orbits) developed in terms of the intersection
between first and second-order mean-motion resonances.

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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: physics