Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Maslov index and spectral counts for linear Hamiltonian systems on
  $\mathbb{R}$   Working with a general class of linear Hamiltonian systems specified on
$\mathbb{R}$, we develop a framework for relating the Maslov index to the
number of eigenvalues the systems have on intervals of the form $[\lambda_1,
\lambda_2)$ and $(-\infty, \lambda_2)$. We verify that our framework can be
implemented for Sturm-Liouville systems, fourth-order potential systems, and a
family of systems nonlinear in the spectral parameter. The analysis is
primarily motivated by applications to the analysis of spectral stability for
nonlinear waves, and aspects of such analyses are emphasized.

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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga