We show that $ L_4 $ and $ L_5 $ in the spatial restricted circular three-body problem are
Nekhoroshev-stable for all but a few values of the reduced mass up to the Routh critical …

Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and
quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in …

Using a scheme given by Lochak, we derive a result of stability over exponentially long
times with respect to the inverse of the distance to an elliptic equilibrium point which has a …

We prove a conjecture by NN Nekhoroshev about the long-time stability of elliptic equilibria
of Hamiltonian systems, without any Diophantine condition on the frequencies. Higher order …

We generalize a sufficient condition for the stability of relative equilibria in symmetric
Hamiltonian systems, due to Patrick (1992 Relative equilibria in Hamiltonian systems: the …

We consider stability of elliptic equilibria in Hamiltonian systems in the frame of
Nekhoroshev's theory, recovering the steepness assumption, in the form of convexity, from …

We apply the spectral formulation of the Nekhoroshev theorem to investigate the longterm
stability of real main belt asteroids. We find numerical indication that some asteroids are in …

We revive the elementary idea of constructing symplectic integrators for Hamiltonian flows
on manifolds by covering the manifold with the charts of an atlas, implementing the algorithm …

In this paper we provide an analytical characterization of the Fourier spectrum of the
solutions of quasi–integrable Hamiltonian systems, which completes the Nekhoroshev …

The purpose of this chapter is to introduce in the simplest possible way the “elements”–ie the
basic facts, ideas, techniques and results–of Hamiltonian perturbation theory. The exposition …