Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Index theory for asymptotic motions under singular potentials   We develop an index theory for parabolic and collision solutions to the
classical n-body problem and we prove sufficient conditions for the finiteness
of the spectral index valid in a large class of trajectories ending with a
total collapse or expanding with vanishing limiting velocities. Both problems
suffer from a lack of compactness and can be brought in a similar form of a
Lagrangian System on the half time line by a regularising change of coordinates
which preserve the Lagrangian structure. We then introduce a Maslov-type index
which is suitable to capture the asymptotic nature of these trajectories as
half-clinic orbits: by taking into account the underlying Hamiltonian structure
we define the appropriate notion of geometric index for this class of solutions
and we develop the relative index theory.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn