The general description of superintegrable systems with one polynomial integral of order N
in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane …

The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian H=
T+ V into a geodesic Hamiltonian T with one additional degree of freedom, is applied to the …

The superintegrability of several Hamiltonian systems defined on three-dimensional
configuration spaces of constant curvature is studied. We first analyze the properties of the …

We study four particular three-dimensional natural Hamiltonian systems defined in
conformally Euclidean spaces. We prove their superintegrability and we obtain, in the four …

We review the results of several of our papers about the procedure of extension of
Hamiltonians, allowing the construction of families of superintegrable systems with non …

Superintegrable Hamiltonian systems in a two-dimensional Euclidean space are
considered. We present all real standard potentials that allow separation of variables in …

The higher order superintegrability of the Tremblay–Turbiner–Winternitz system (related to
the harmonic oscillator) is studied on the two-dimensional spherical and hyperbolic spaces …

If we take a superintegrable Stäckel system and make variables “faster” or “slower,” that is,
equivalent to a trivial transformation of the Stäckel matrix and potentials, then we obtain an …

Two important advances in integrability have been the recent discovery of the higher-order
superintegrability of the Tremblay–Turbiner–Winternitz system (related to the harmonic …

Nonlinearity 36 (2023) 1143 A Blasco et al perturbations of the classical Zernike system.
Finally, it is shown that HN (and so the Zernike system as well) is endowed with a Poisson sl …