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

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.