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Super-exponential stability for generic real-analytic elliptic equilibrium points

Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent (2020), Super-exponential stability for generic real-analytic elliptic equilibrium points, Advances in Mathematics, 366. 10.1016/j.aim.2020.107088

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Advances in Mathematics
Volume
366
Publisher
Elsevier
Publication identifier
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Author(s)
Bounemoura, Abed
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Fayad, Bassam
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Niederman, Laurent
Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
Abstract (EN)
We consider the dynamics in a neighborhood of an elliptic equilibrium point with a Diophantine frequency of a symplectic real analytic vector field and we prove the following result of effective stability. Generically, both in a topological and measure-theoretical sense, any solution starting sufficiently close to the equilibrium point remains close to it for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the equilibrium point.
Subjects / Keywords
Hamiltonian systems; Stability theory; Equilibrium points