Analyse et dynamique

Asymptotically quasiperiodic solutions for time-dependent Hamiltonians

by Mr Donato Scarcella (Université Paris Dauphine-PSL)

Salle 1 (LJAD)

Salle 1



In 1954 Kolmogorov laid the foundation for the so-called KAM theory. This theory shows the persistence of quasiperiodic solutions in nearly integrable Hamiltonian systems. It is motivated by classical problems in celestial mechanics, such as the n-body problem.




In this talk, we are interested in perturbations which depend on time non-quasiperiodically. More specifically, we consider time-dependent perturbations of Hamiltonians having an invariant torus supporting quasiperiodic solutions. Assuming the perturbation decays polynomially fast as time tends to infinity, we prove the existence of orbits converging, as time tends to infinity, to the quasiperiodic motions of the unperturbed system. 




We will apply these results to the example of a planetary system perturbed by a given comet coming from and going back to infinity asymptotically along a hyperbolic Keplerian orbit.