The Kepler problem: polynomial algebra of non-polynomial first integrals

A. V. Tsiganov

doi:10.1134/s1560354719040014

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arXiv · 1903.08846

The Kepler problem: polynomial algebra of non-polynomial first integrals

A. V. Tsiganov

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Abstract

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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A. V. Tsiganov. 2019-03-21. The Kepler problem: polynomial algebra of non-polynomial first integrals. https://doi.org/10.1134/s1560354719040014

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