23 citations · 116 across the 28 of their papers we have counts for
6 papers · 1 filter
Generic perturbations of linear integrable Hamiltonian systems
Abed Bounemoura
In this paper, we investigate perturbations of linear integrable Hamiltonian systems, with the aim of establishing results in the spirit of the KAM theorem (preservation of invaria…
Double exponential stability for generic real-analytic elliptic equilibrium points
Abed Bounemoura, Bassam Fayad, Laurent Niederman
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 resul…
Nekhoroshev's estimates for quasi-periodic time-dependent perturbations
Abed Bounemoura
In this paper, we consider a Diophantine quasi-periodic time-dependent analytic perturbation of a convex integrable Hamiltonian system, and we prove a result of stability of the ac…
Ergodization time for linear flows on tori via geometry of numbers
Abed Bounemoura
In this paper, we give a new, short, simple and geometric proof of the optimal er-godization time for linear flows on tori. This result was first obtained by Bourgain, Golse and We…
A note on micro-instability for Hamiltonian systems close to integrable
Abed Bounemoura, Vadim Kaloshin
In this note, we consider the dynamics associated to an epsilon-perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and…
Instability of resonant invariant tori in Hamiltonian systems
Abed Bounemoura
In this article, we consider the dynamics in a neighborhood of a quasi-periodic torus which is invariant by a Hamiltonian flow, we discuss several notions of stability and we prove…