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math.DS2010
An example of instability in high-dimensional Hamiltonian systems
Abed Bounemoura
In this article, we use a mechanism introduced by Herman, Marco and Sauzin to show that if a perturbation of a quasi-convex integrable Hamiltonian system is not too small with resp…
math.DS2010
Improved exponential stability for near-integrable quasi-convex Hamiltonians
Abed Bounemoura, Jean-Pierre Marco
In this article, we improve previous results on exponential stability for analytic and Gevrey perturbations of quasi-convex integrable Hamiltonian systems. In particular, this prov…
math.DS2010★ 2 cited
Nekhoroshev estimates for finitely differentiable quasi-convex Hamiltonians
Abed Bounemoura
A major result concerning perturbations of integrable Hamiltonian systems is given by Nekhoroshev estimates, which ensures exponential stability of all solutions provided the syste…