Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Integrability of the Geodesic Flow on a
  Friedmann-Robertson-Walker Spacetime   We study the geodesic flow on the cotangent bundle of a
Friedman-Robertson-Walker spacetime (M, g). On this bundle, the HamiltonJacobi
equation is completely separable and this separability leads us to construct
four linearly independent integrals in involution i.e. Poisson commuting
amongst themselves and pointwise linearly independent. These integrals involve
the six linearly independent Killing fields of the background metric g. As a
consequence, the geodesic flow on an FRW background is completely integrable in
the Liouville-Arnold sense. For the case of a spatially closed universe we
construct families of invariant by the flow sub manifolds.

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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: math
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The categories of this paper are: stat
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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: acc-phys