Geodesic
Superintegrable systems with algebraic and rational integrals of motion
Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 218-234

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We consider superintegrable deformations of the Kepler problem and the harmonic oscillator on the plane and also superintegrable metrics on a two-dimensional sphere, for which the additional integral of motion is either an algebraic or a rational function of momenta. According to Euler, these integrals of motion take the simplest form in terms of affine coordinates of elliptic curve divisors.
Keywords: finite-dimensional integrable system, discrete integrable map, intersection theory. 
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     author = {A. V. Tsiganov},
     title = {Superintegrable systems with algebraic and rational integrals of motion},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {218--234},
     publisher = {mathdoc},
     volume = {199},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a3/}
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A. V. Tsiganov. Superintegrable systems with algebraic and rational integrals of motion. Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 218-234. http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a3/