Nonlinear stability around an elliptic equilibrium point in a Hamiltonian system

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 definite torsion. At the price of this assumption, our study is valid without arithmetical properties of the linearized system while the previous theorems of this kind rely on a Diophantine condition on the linear spectrum. Actually, under the latter condition and a definite torsion, a result of stability over superexponentially long times can be proved. Finally, the same kind of theorems are also valid for an elliptic lower-dimensional invariant torus.