Bi-Hamiltonian structure as a shadow of non-Noether symmetry.
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian Systems with convex Hamiltonians.
Characterization of diffeomorphisms that are symplectomorphisms
Let and be compact symplectic manifolds (resp. symplectic manifolds) of dimension 2n > 2. Fix 0 < s < n (resp. 0 < k ≤ n) and assume that a diffeomorphism Φ : X → Y maps all 2s-dimensional symplectic submanifolds of X to symplectic submanifolds of Y (resp. all isotropic k-dimensional tori of X to isotropic tori of Y). We prove that in both cases Φ is a conformal symplectomorphism, i.e., there is a constant c ≠0 such that .
Classification géométrique des structures internes des systèmes dynamiques à deux spins
Closed Curves on Convex Hypersurfaces and Periods of Nonlinear Oscillations.
Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems
Comment by the editors on the paper : “The hamiltonian formalism in higher order variational problems”
Completely Integrable Hamiltonian Systems Connected with Semisimple Lie Algebras.
Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques
Dans cet article nous généralisons les résultats obtenus par J. Chazarain sur le spectre d’opérateurs de Schrödinger lorsque . Nous étendons ses résultats aux opérateurs pseudo-différentiels globalement elliptiques d’ordre .
Connections and regularity on the tangent and cotangent bundle.
Contribution to Theory of First Integrals for Nonholonomic Mechanical Systems
Convergence results for periodic solutions of nonautonomous Hamiltonian systems
We prove some stability results for a certain class of periodic solutions of nonautonomous Hamiltonian systems in the case of Hamiltonian functions either with subquadratic growth or homogeneous with superquadratic growth. Thus we extend to the nonautonomous case some results recently established by the Authors for the autonomous case.
Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems.
Drift and diffusion in phase space
Errata : «Classification géométrique des structures internes des systèmes dynamiques à 2 spins»
Erratum for "Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature".
A mistake was found in the reasoning leading to a Lagrangian which we considered as equivalent from the formula for the action S(γ) below the classical mechanical problem (3) on "Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature", page 271.
Existence of solutions for a nonlinear discrete system involving the -Laplacian
The existence of solutions for boundary value problems for a nonlinear discrete system involving the -Laplacian is investigated. The approach is based on critical point theory.
Explicit Solutions of Classical Generalized Toda Models.
First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems.
Generalized polarized manifolds.