Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Conley-Zehnder index   The Conley-Zehnder index associates an integer to any continuous path of
symplectic matrices starting from the identity and ending at a matrix which
does not admit 1 as an eigenvalue. We give new ways to compute this index.
Robbin and Salamon define a generalization of the Conley-Zehnder index for any
continuous path of symplectic matrices; this generalization is half integer
valued. It is based on a Maslov-type index that they define for a continuous
path of Lagrangians in a symplectic vector space $(W,\bar{\Omega})$, having
chosen a given reference Lagrangian $V$. Paths of symplectic endomorphisms of
$(\R^{2n},\Omega_0)$ are viewed as paths of Lagrangians defined by their graphs
in $(W=\R^{2n}\oplus \R^{2n},\bar{\Omega}=\Omega_0\oplus -\Omega_0)$ and the
reference Lagrangian is the diagonal. Robbin and Salamon give properties of
this generalized Conley-Zehnder index and an explicit formula when the path has
only regular crossings. We give here an axiomatic characterization of this
generalized Conley-Zehnder index. We also give an explicit way to compute it
for any continuous path of symplectic matrices.

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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th