Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kepler problem: polynomial algebra of non-polynomial first integrals   The sum of elliptic integrals simultaneously determines orbits in thr Kepler
problem and the addition of divisors on elliptic curves. Periodic motion of a
body in physical space is defined by symmetries, whereas periodic motion of
divisors is defined by a fixed point on the curve. Algebra of the first
integrals associated with symmetries is a well-known mathematical object,
whereas algebra of the first integrals associated with coordinates of fixed
points is unknown. In this paper, we discuss polynomial algebras of
non-polynomial first integrals of superintegrable systems associated with
elliptic curves.

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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: econ