Representation of non-Hamiltonian vector fields in the coordinates of the observer via the isosymplectic geometry.
Representation theory of finite Abelian groups applied to a linear diatomic crystal.
Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé
Henri Poincaré avait déjà remarqué que les variétés stable et instable du pendule perturbé, défini par l’hamiltonienne coïncident pas lorsque que le paramètre n’est pas nul, mais qu’on peut leur associer un même développement formel divergent en puissance de . Cette divergence est ici analysée au moyen de la récente théorie de la résurgence, et du calcul étranger qui permet de trouver un équivalent asymptotique de l’écart des deux variétés pour tendant vers zéro - du moins cela est-il montré...
Root systems and hypergeometric functions IV
Rotation numbers for Lagrangian systems and Morse theory
Singular Bohr–Sommerfeld rules for 2D integrable systems
Singular fibres of the momentum mapping for integrable Hamiltonian systems.
Singular Hamiltonian systems and symplectic capacities
The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation which nevertheless...
Sobre los sistemas mecánicos con enlaces.
A mathematical model is proposed in order to describe the behaviour of mechanical systems with constraints.
Solutions d'équations d'Hamilton-Jacobi et géométrie symplectique
Solutions of DEs and PDEs as potential maps using first order Lagrangians.
Solutions périodiques de systèmes hamiltoniens
Some affine properties of the -symplectic manifolds.
Some examples of nonsingular Morse-Smale vector fields on
One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of...
Some remarks on -webs of complex surfaces, and a problem posed by D. Cerveau. (Quelques remarques sur les -webs des surfaces complexes et un problème proposé par D. Cerveau.)
Some remarks on symplectic actions of compact groups.
Some results on connecting orbits for a class of Hamiltonian systems.
Some results on the calculus of variations on jet spaces
Spectral curves and integrable systems
Spectre des opérateurs elliptiques et flots hamiltoniens