Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems

By Jean-Pierre Marco, D. Sauzin. 2003

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Speed of Arnold diffusion for analytic Hamiltonian systems (2011, methodology): “Continuing the work started by Herman, Marco and Sauzin (see [ 16 ]) extended the Nekhoroshev theorem to Gevrey-α class and constructed an example of quasi-convex system and an orbit exhibiting Arnold diffusion with T( � ≤ exp(C� −”
KAM theorem for Gevrey Hamiltonians (2003, methodology): “Effective stability of the action along all the trajectories for Gevrey smooth Hamiltonians has been obtained recently by Marco and Sauzun [10].”
The dynamics of pseudographs in convex Hamiltonian systems (2004, background): “See [1] and [22] for beautiful and deep examples of perturbations of fully integrable systems.”