TY - JOUR

T1 - The Kepler Problem

T2 - Polynomial Algebra of Nonpolynomial First Integrals

AU - Tsiganov, Andrey V.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - 33E05

KW - 37E99

KW - 70H12

KW - algebra of first integrals

KW - divisor arithmetic

UR - http://www.scopus.com/inward/record.url?scp=85070200431&partnerID=8YFLogxK

U2 - 10.1134/S1560354719040014

DO - 10.1134/S1560354719040014

M3 - Article

AN - SCOPUS:85070200431

VL - 24

SP - 353

EP - 369

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

SN - 1560-3547

IS - 4

ER -