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Superexponential Stability of Quasi-Periodic Motion in Hamiltonian Systems

Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent (2017), Superexponential Stability of Quasi-Periodic Motion in Hamiltonian Systems, Communications in Mathematical Physics, 350, 1, p. 361–386. 10.1007/s00220-016-2782-9

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
Communications in Mathematical Physics
Volume
350
Number
1
Publisher
Springer
Pages
361–386
Publication identifier
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Author(s)
Bounemoura, Abed
Fayad, Bassam
Niederman, Laurent
Abstract (EN)
We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the torus. We also prove that for an arbitrary small perturbation of a generic integrable Hamiltonian system, there is a set of almost full positive Lebesgue measure of KAM tori which are doubly exponentially stable. Our results hold true for real-analytic but more generally for Gevrey smooth systems.
Subjects / Keywords
Hamiltonian systems