Approximation of invariant surfaces by periodic orbits in high-dimensional maps: Some rigorous results.
Area preserving homeomorphisms of open surfaces of genus zero.
Arnold diffusion: a variational construction.
Asymptotic solutions for large time of Hamilton–Jacobi equations in euclidean n space
Basics of Lagrangian foliations.
The paper is an exposition of basic known local and global results on Lagrangian foliations such as the Theorem of Darboux-Lie, Weinstein, Arnold-Liouville, a global characterization of cotangent bundles, higher order Maslov classes, etc.
Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential
Bifurcation d'orbites périodiques d'un système hamiltonien au voisinage d'une position d'équilibre
Bifurcations and Hamilton's Principle.
Birational equivalence in the symplectic category.
Birkhoff normal formsand analytic geometry
Blow up of mechanical systems with a homogeneous energy.
By using the ideas introduced by McGehee in the study of the singularities in some problems of Celestial Mechanics, we study the singularities at the origin and at the infinity for some classical mechanical systems with homogeneous kinetic and potential energy functions. For these systems the origin and the infinity of the configuration coordinates is usually a singularity or a nullity of the Hamiltonian function and the verctor field. This work generalizes a previous one by the first and the third...
Borel summation and splitting of separatrices for the Hénon map
We study two complex invariant manifolds associated with the parabolic fixed point of the area-preserving Hénon map. A single formal power series corresponds to both of them. The Borel transform of the formal series defines an analytic germ. We explore the Riemann surface and singularities of its analytic continuation. In particular we give a complete description of the “first” singularity and prove that a constant, which describes the splitting of the invariant manifolds, does not vanish. An interpretation...
Canonical realizations of Lie algebras associated with foliated coadjoint orbits
Capacités symplectiques et applications
Caractérisation variationnelle globale des flots canoniques et de contact dans leurs groupes de difféomorphismes
Chapitre VI Compactification d’actions de et variables action-angle avec singularités
Characterization of higher-order tangent bundles.
Classes caractéristiques des couples de sous-fibrés lagrangiens
La classe de Maslov, classe de cohomologie entière de degré 1, définie sur un fibré vectoriel symplectique muni de deux champs de plans lagrangiens, est une obstruction à leur transversalité. L’objet de ce travail est de construire explicitement, en termes de formes différentielles, des obstructions cohomologiques analogues (de degré supérieur). On étudie de ce point de vue les sous-variétés lagrangiennes de .
Classes caractéristiques isotropes.
Classes isotropes et classes de Maslov