Asymptotically quasiperiodic solutions for time-dependent Hamiltonians
Abstract
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 goes to infinity) exponentially fast in time, they proved the existence of motions converging in time (when t goes to infinity) to quasiperiodic solutions associated with the unperturbed system (asymptotically quasiperiodic solutions). In this paper, we generalize this result in the particular case of time-dependent 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.
Cite
@article{arxiv.2211.06623,
title = {Asymptotically quasiperiodic solutions for time-dependent Hamiltonians},
author = {Donato Scarcella},
journal= {arXiv preprint arXiv:2211.06623},
year = {2022}
}