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

Abed Bounemoura (1) , Bassam Fayad (2) , Laurent Niederman (3, 4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides
4 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Domaines: Systèmes dynamiques [math.DS]

Abed Bounemoura, Bassam Fayad, Laurent Niederman. Super-exponential stability for generic real-analytic elliptic equilibrium points. 2015. ⟨hal-01188980v1⟩