Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three.
Quadratic and homogeneous Hamilton-Poisson systems on .
Quantification géométrique et réduction symplectique
Quantum deformations and superintegrable motions on spaces with variable curvature.
Quantum integrable systems
Quantum super-integrable systems as exactly solvable models.
Quasistable gradient and Hamiltonian systems with a pairwise interaction randomly perturbed by Wiener processes.
Quelques invariants topologiques en géométrie symplectique
Randomly connected dynamical systems - asymptotic stability
We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.
Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension
We study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint -pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational tori, we obtain an accurate description of the spectrum in a suitable complex window, provided that the...
Recent results in symplectic geometry
Recent results on the separatrix splitting for the standard map
Reconstruction phases for Hamiltonian systems on cotangent bundles.
Réductibilité de systèmes dynamiques variationnels
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric
For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric
For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential...
Reduction of complex Poisson manifolds.
Reduction of Hamiltonian Systems, Affine Lie Algebras and Lax Equations II.
Reduction of Hamiltonian Systems, Affine Lie Algebras and Lax Equations.
Régularisation d'équations de Stratonovitch à sauts entre variétés