Scalar-flat Kähler metrics with SU (2) symmetry.
Second order superintegrable systems in three dimensions.
Separation of variables and the geometry of Jacobians.
Singularities of momentum maps of integrable Hamiltonian systems with two degrees of freedom.
Solvability of the super KP equation and a generalization of the Birkhoff decomposition.
Some orthogonal polynomials in four variables.
Structure theory for second order 2D superintegrable systems with 1-parameter potentials.
Summability of first integrals of a -non-integrable resonant Hamiltonian system
This article studies the summability of first integrals of a -non-integrable resonant Hamiltonian system. The first integrals are expressed in terms of formal exponential transseries and their Borel sums. Smooth Liouville integrability and a relation to the Birkhoff transformation are discussed from the point of view of the summability.
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...
Superintegrability on three-dimensional Riemannian and relativistic spaces of constant curvature.
Superintegrable oscillator and Kepler systems on spaces of nonconstant curvature via the Stäckel transform.
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 le spectre semi-classique d’un système intégrable de dimension 1 autour d’une singularité hyperbolique
Dans cet article on décrit le spectre semi-classique d’un opérateur de Schrödinger sur avec un potentiel type double puits. La description qu’on donne est celle du spectre autour du maximum local du potentiel. Dans la classification des singularités de l’application moment d’un système intégrable, le double puits représente le cas des singularités non-dégénérées de type hyperbolique.
Symplectic topology of integrable hamiltonian systems, I : Arnold-Liouville with singularities
Systèmes hamiltoniens complètement intégrables et déformations d'algèbres de Lie.
Some of the completely integrable Hamiltonian systems obtained through Adler-Kostant-Symes theorem rely on two distinct Lie algebra structures on the same underlying vector space. We study here the cases when two structures are linked together by deformations.
Systèmes hamiltoniens k-symplectiques.
We study some properties of the k-symplectic Hamiltonian systems in analogy with the well-known classical Hamiltonian systems. The integrability of k-symplectic Hamiltonian systems and the relationships with the Nambu's statistical mechanics are given.
Systèmes intégrables à -corps sur la droite
Systems of Toda Type, Inverse Spectral Problems, and Representation Theory.