Abstract (EN)

In 2015, M. Canadell and R. de la Llave consider a time-dependent perturbation of a vector field having an invariant torus supporting quasiperiodic solutions. Under a smallness assumption on the perturbation and assuming the perturbation decays (when t → +∞) exponentially fast in time, they proved the existence of motions converging in time (when t → +∞) to quasiperiodic solutions associated with the unperturbed system (asymptotically quasiperiodic solutions). In this paper, we generalize this result in the particular case of timedependent Hamiltonian systems. The exponential decay in time is relaxed (due to the geometrical properties of Hamiltonian systems) and the smallness assumption on the perturbation is removed.