Algebraic calculation of the energy eigenvalues for the nondegenerate three-dimensional Kepler-Coulomb potential.
Algebraic complete integrability of an integrable system of Beauville
We show that the Beauville’s integrable system on a ten dimensional moduli space of sheaves on a K3 surface constructed via a moduli space of stable sheaves on cubic threefolds is algebraically completely integrable, using O’Grady’s construction of a symplectic resolution of the moduli space of sheaves on a K3.
Algebraic integrability of Schrodinger operators and representations of Lie algebras
Algebraic non-integrability of the Cohen map.
Algebraically completely integrable systems and Kummer varieties.
Algebras of integrals
Algèbres de Lie, systèmes hamiltoniens, courbes algébriques
Algebro-geometric Approach to the Yang-Baxter Equation and Related Topics
Almost contact structures and time-dependent Lagrangians
Almost product structures and Poisson reduction of presymplectic systems.
An alternative canonical approach to the ghost problem in a complexified extension of the Pais-Uhlenbeck oscillator.
An existence result on periodic solutions of an ordinary -Laplacian system.
An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models.
An Index Theory and Existence of Multiple Brake Orbits for Star-Shaped Hamiltonian Systems
An integrable flow on a family of Hilbert Grassmannians.
Analytic invariants for the resonance
Associated to analytic Hamiltonian vector fields in having an equilibrium point satisfying a non semisimple resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.
Anosov flows and non-Stein symplectic manifolds
We simplify and generalize McDuff’s construction of symplectic 4-manifolds with disconnected boundary of contact type in terms of the linking pairing defined on the dual of 3-dimensional Lie algebras. This leads us to an observation that an Anosov flow gives rise to a bi-contact structure, i.e. a transverse pair of contact structures with different orientations, and the construction turns out to work for 3-manifolds which admit Anosov flows with smooth invariant volume. Finally, new examples of...
Another approach to the classical calculus of variations. I
Another approach to the classical calculus of variations. III
Another approach to the classical calculus of variations. II. Hamiltonian theory