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The Kepler Problem: Polynomial Algebra of Nonpolynomial First Integrals

The Kepler Problem: Polynomial Algebra of Nonpolynomial First Integrals The sum of elliptic integrals simultaneously determines orbits in the 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. The algebra of the first integrals associated with symmetries is a well-known mathematical object, whereas the algebra of the first integrals associated with the coordinates of fixed points is unknown. In this paper, we discuss polynomial algebras of nonpolynomial first integrals of superintegrable systems associated with elliptic curves. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

The Kepler Problem: Polynomial Algebra of Nonpolynomial First Integrals

Regular and Chaotic Dynamics , Volume 24 (4) – Aug 6, 2019

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References (49)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354719040014
Publisher site
See Article on Publisher Site

Abstract

The sum of elliptic integrals simultaneously determines orbits in the 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. The algebra of the first integrals associated with symmetries is a well-known mathematical object, whereas the algebra of the first integrals associated with the coordinates of fixed points is unknown. In this paper, we discuss polynomial algebras of nonpolynomial first integrals of superintegrable systems associated with elliptic curves.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Aug 6, 2019

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