
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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Article accepté pour publication ou publiéDate
2020Journal name
Advances in MathematicsVolume
366Publisher
Elsevier
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Bounemoura, AbedCEntre 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 pointsRelated items
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