Algèbres de Lie, systèmes hamiltoniens, courbes algébriques
Algebro-geometric Integration in Classical and Statistical Mechanics
Almost product structures and Poisson reduction of presymplectic systems.
An affine framework for analytical mechanics
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.
An alternative canonical approach to the ghost problem in a complexified extension of the Pais-Uhlenbeck oscillator.
An expression of classical dynamics
Another approach to the classical calculus of variations. I
Another approach to the classical calculus of variations. III
Another approach to the classical calculus of variations. II. Hamiltonian theory
Applications numériques de la dualité en mécanique hamiltonienne
Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group
We propose and analyze numerical schemes for viscosity solutions of time-dependent Hamilton-Jacobi equations on the Heisenberg group. The main idea is to construct a grid compatible with the noncommutative group geometry. Under suitable assumptions on the data, the Hamiltonian and the parameters for the discrete first order scheme, we prove that the error between the viscosity solution computed at the grid nodes and the solution of the discrete problem behaves like where h is the mesh step. Such...
Arnold diffusion: a variational construction.