Elliptic curve arithmetic and superintegrable systems (1810.11991v2)

Published 29 Oct 2018 in nlin.SI, math-ph, math.DS, and math.MP

Abstract: Harmonic oscillator and the Kepler problem are superintegrable systems which admit more integrals of motion than degrees of freedom and all these integrals are polynomials in momenta. We present superintegrable deformations of the oscillator and the Kepler problem with algebraic and rational first integrals. Also, we discuss a family of superintegrable metrics on the two-dimensional sphere, which have similar first integrals.

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Authors (1)

A. V. Tsiganov

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