La réduction symplectique appliquée à la non-intégrabilité du problème du satellite
La théorie des perturbations au voisinage des systèmes hamiltoniens convexes
Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations
We propose a Lagrangian approach to deriving energy-preserving finite difference schemes for the Euler–Lagrange partial differential equations. Noether’s theorem states that the symmetry of time translation of Lagrangians yields the energy conservation law. We introduce a unique viewpoint on this theorem: “the symmetry of time translation of Lagrangians derives the Euler–Lagrange equation and the energy conservation law, simultaneously.” The proposed method is a combination of a discrete counter...
Lagrangian theory for presymplectic systems
Lagrangians and hamiltonians on affine bundles and higher order geometry
The higher order bundles defined by an anchored bundle are constructed as a natural extension of the higher tangent spaces of a manifold. We prove that a hyperregular lagrangian (hyperregular affine hamiltonian) is a linearizable sub-lagrangian (affine sub-hamiltonian) on a suitable Legendre triple.
Lagrangians and higher order tangent spaces.
Le formalisme de contact en mécanique classique et relativiste
Le problème de Cauchy pour les équations de Hamilton-Jacobi-Bellman
Lepagean 2-forms in higher order Hamiltonian mechanics. I. Regularity
Lepagean 2-forms in higher order Hamiltonian mechanics. II. Inverse problem
Levi-flat invariant sets of holomorphic symplectic mappings
We classify four families of Levi-flat sets which are defined by quadratic polynomials and invariant under certain linear holomorphic symplectic maps. The normalization of Levi- flat real analytic sets is studied through the technique of Segre varieties. The main purpose of this paper is to apply the Levi-flat sets to the study of convergence of Birkhoff's normalization for holomorphic symplectic maps. We also establish some relationships between Levi-flat invariant sets...
Lie algebroids and mechanics
We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold ; the set of units is the zero section identified with the manifold . We study the Legendre transformation on Lie algebroids.
Lie algebroids in classical mechanics and optimal control.
Lie point Symmetries of Hamiltonian Systems
Los Espacios de Hilbert-Lobatschewsky. La masa de un gas relativista. Las ondas relativistas de materia.