Géométrie algébrique de Poisson et déformations
Géométrie des équations différentielles du second ordre
Geometry of invariant tori of certain integrable systems with symmetry and an application to a nonholonomic system.
Geometry of non-holonomic diffusion
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.
Geometry of Poisson structures.
Geometry on the group of Hamiltonian diffeomorphisms.
Graded Poisson structures on the algebra of differential forms.
Gradient homotopies of gradient vector fields
Gradient-Like and Integrable Vector Fields on IR2.
Gradients and canonical transformations
The main aim of this paper is to give some counterexamples to global invertibility of local diffeomorphisms which are interesting in mechanics. The first is a locally strictly convex function whose gradient is non-injective. The interest in this function is related to the Legendre transform. Then I show two non-injective canonical local diffeomorphisms which are rational: the first is very simple and related to the complex cube, the second is defined on the whole ℝ⁴ and is obtained from a recent...
Gromov's K-Area and Symplectic Rigidity.
Group Actions on Strongly Monotone Dynamical Systems.
Groupoïde d'homotopie d'un feuilletage Riemannien et réalisation symplectique de certaines variétés de Poisson.
The purpose of this paper is to prove the existence of a symplectic realization for a large class of regular Poisson manifolds with Riemannian two dimensional characteristic foliation. To do so, we will show that the homotopy groupoid of a Riemannian foliation is locally trivial.
Groupoïdes symplectiques
Hamiltonian Diffeomorphisms and Lagrangian Distributions.
Hamiltonian loops from the ergodic point of view
Let be the group of Hamiltonian diffeomorphisms of a closed symplectic manifold . A loop is called strictly ergodic if for some irrational number the associated skew product map defined by is strictly ergodic. In the present paper we address the following question. Which elements of the fundamental group of can be represented by strictly ergodic loops? We prove existence of contractible strictly ergodic loops for a wide class of symplectic manifolds (for instance for simply connected...
Hamiltonian stability and subanalytic geometry
In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry, we derive a geometric criterion for steepness: a numerical function which is real analytic around a...
Hamiltonian Systems: Generic Properties of Closed Orbits and Local Perturbations.
Hamiltonian systems, Lagrangian tori and Birkhoffs's theorem.
Hamiltonian systems with linear potential and elastic constraints
We consider a class of Hamiltonian systems with linear potential, elastic constraints and arbitrary number of degrees of freedom. We establish sufficient conditions for complete hyperbolicity of the system.