Double exponential stability for generic real-analytic elliptic equilibrium points

Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent

Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent (2015), Double exponential stability for generic real-analytic elliptic equilibrium points. https://basepub.dauphine.fr/handle/123456789/17158

Type

Document de travail / Working paper

External document link

https://hal.archives-ouvertes.fr/hal-01188980

Date

2015

Series title

Cahier de recherche CEREMADE, Université Paris-Dauphine

Metadata

Show full item record

Author(s)

Bounemoura, Abed
Fayad, Bassam
Niederman, Laurent

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. We actually prove a more general statement assuming the frequency is only non-resonant. This improves previous results where much stronger non-generic assumptions were required.

Subjects / Keywords

elliptic equilibrium points