Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The semi-classical Maupertuis-Jacobi correspondence: stable and unstable
  spectra   We investigate semi-classical properties of Maupertuis-Jacobi correspondence
for families of 2-D Hamiltonians $(H_\lambda(x,\xi), {\cal H}_\lambda(x,\xi))$,
when ${\cal H}_\lambda(x,\xi)$ is the perturbation of a completely integrable
Hamiltonian $\widetilde{\cal H}$ veriying some isoenergetic non-degeneracy
conditions. Assuming $\hat H_\lambda$ has only discrete spectrum near $E$, and
the energy surface $\{\widetilde{\cal H}_0={\cal E}\}$ is separated by some
pairwise disjoint Lagrangian tori, we show that most of eigenvalues for $\hat
H_\lambda$ near $E$ are asymptotically degenerate as $h\to0$. This applies in
particular for the determination of trapped modes by an island, in the linear
theory of water-waves. We also consider quasi-modes localized near rational
tori. Finally, we discuss breaking of Maupertuis-Jacobi correspondence on the
equator of Katok sphere.

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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas