Asymptotic KAM tori for time-dependent Hamiltonians
Scarcella, Donato (2022), Asymptotic KAM tori for time-dependent Hamiltonians. https://basepub.dauphine.psl.eu/handle/123456789/24100
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Document de travail / Working paperDate
2022Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSLPublished in
Paris
Pages
37
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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.Related items
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