The Kepler problem is a dynamical system that is well defined not only on the Euclidean
plane but also on the sphere and on the hyperbolic plane. First, the theory of central …

The existence of superintegrable systems with n= 2 degrees of freedom possessing three
independent globally defined constants of motion which are quadratic in the velocities is …

We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb
systems, replacing their angular degrees of freedom by those of a generalized rational …

The higher order superintegrability of separable potentials is studied. It is proved that these
potentials possess (in addition to the two quadratic integrals) a third integral of higher order …

Two Harmonic Oscillators (isotropic and nonisotropic 2: 1) are studied on the two-
dimensional sphere S 2 and the hyperbolic plane H 2. Both systems are integrable and …

We present a general scheme for constructing the Poisson structure of super-integrable
dynamical systems of which the rational Calogero–Moser system is the most interesting one …

We construct the Hamiltonians and symmetry generators of Calogero-oscillator and
Calogero-Coulomb models on the N-dimensional sphere within the matrix-model reduction …

The properties of several noncentral n= 2 harmonic oscillators are examined on spaces of
constant curvature. All the mathematical expressions are presented using the curvature κ as …

The higher order superintegrability of systems separable in polar coordinates is studied
using an approach that was previously applied for the study of the superintegrability of a …

The theory of dynamical but non-Cartan (or non-Noether) symmetries is studied using the
symplectic formalism approach. It is shown that the superintegrability of the n-dimensional …