Singularities of momentum maps of integrable Hamiltonian systems with two degrees of freedom.
Superintegrability and time-dependent integrals
While looking for additional integrals of motion of several minimally superintegrable systems in static electric and magnetic fields, we have realized that in some cases Lie point symmetries of Euler-Lagrange equations imply existence of explicitly time-dependent integrals of motion through Noether’s theorem. These integrals can be combined to get an additional time-independent integral for some values of the parameters of the considered systems, thus implying maximal superintegrability. Even for...
Superintegrable Potentials and superposition of Higgs Oscillators on the Sphere S²
The spherical version of the two-dimensional central harmonic oscillator, as well as the spherical Kepler (Schrödinger) potential, are superintegrable systems with quadratic constants of motion. They belong to two different spherical "Smorodinski-Winternitz" families of superintegrable potentials. A new superintegrable oscillator have been recently found in S². It represents the spherical version of the nonisotropic 2:1 oscillator and it also belongs to a spherical family of quadratic superintegrable...
Sur les intégrales premières symétriques du flot géodésique.
Symmetry operators for the Fokker-Planck-Kolmogorov equation with nonlocal quadratic nonlinearity.