On the Mishchenko–Fomenko hypothesis for a generalized oscillator and Kepler system

Abstract

Deformations of the Kepler problem and the harmonic oscillator are considered for which
additional integrals of motion are the coordinates of the reduced divisor, according to the
Riemann–Roch theorem. For this family of non-commutative integrable systems the validity of
the Mishchenko–Fomenko hypothesis about the existence of integrals of motion from a single
functional class, in this case polynomial integrals of motion, is discussed.