The Painlevé III equation and the Iwasawa decomposition.
The real-analytic solutions of the Abel functional equation
For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.
The reduction of symplectic structure and Sternberg construction
The singularities of Yang-Mills connections for bundles on a surface.
The Surgery of Lagrange Submanifolds.
The symbol of a lagrangian distribution
The symplectic geometry of affine connenctions on surfaces.
The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics
The tiered Aubry set for autonomous Lagrangian functions
Let be a Tonelli Lagrangian function (with compact and connected and ). The tiered Aubry set (resp. Mañé set) (resp. ) is the union of the Aubry sets (resp. Mañé sets) (resp. ) for closed 1-form. Then1.the set is closed, connected and if , its intersection with any energy level is connected and chain transitive;2.for generic in the Mañé sense, the sets and have no interior;3.if the interior of is non empty, it contains a dense subset of periodic points.We then give an example...
The topological behaviour of a diffeomorphism near a fixed point.
The Weinstein conjecture in cotangent bundles and related results
The Weinstein Conjecture in P X Cl.
Théorie des groupoïdes symplectiques
Thom polynomials for open Whitney umbrellas of isotropic mappings
A smooth mapping of a smooth n-dimensional manifold L into a smooth 2n-dimensional symplectic manifold (M,ω) is called isotropic if f*ω vanishes. In the last ten years, the local theory of singularities of isotropic mappings has been rapidly developed by Arnol’d, Givental’ and several authors, while it seems that the global theory of their singularities has not been well studied except for the work of Givental’ [G1] in the case of dimension 2 (cf. [A], [Au], [I2], [I-O]). In the present paper,...
Three periodic solutions to an eigenvalue problem for a class of second-order Hamiltonian systems.
Time-dependent circular billiard.
Topological Classification of Linear Endomorphisms.
Topology and Mechanics. II. The Planar n-Body Problem.
Topology of vortices
Tores invariants des systèmes dynamiques hamiltoniens