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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Asymptotically quasiperiodic solutions for time-dependent Hamiltonians

Résumé

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 an asymptotic KAM torus. An asymptotic KAM torus is a time-dependent family of embedded tori converging in time to the invariant torus associated with the unperturbed system. 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.
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Dates et versions

hal-03849794 , version 1 (12-11-2022)
hal-03849794 , version 2 (30-01-2023)

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  • HAL Id : hal-03849794 , version 2

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Donato Scarcella. Asymptotically quasiperiodic solutions for time-dependent Hamiltonians. 2023. ⟨hal-03849794v2⟩
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