Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hamiltonian Dynamics of Magnetic Confinement in Toroidal Domains   We consider a class of magnetic fields defined over the interior of a
manifold $M$ which go to infinity at its boundary and whose direction near the
boundary of $M$ is controlled by a closed 1-form $\sigma_\infty \in
\Gamma(T^*\partial M)$. We are able to show that charged particles in the
interior of $M$ under the influence of such fields can only escape the manifold
through the zero locus of $\sigma_\infty$. In particular in the case where the
1-form is nowhere vanishing we conclude that the particles become confined to
its interior for all time.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con