Abstract: | In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems,
and we will construct an example of instability showing that both our result and our example are optimal. Moreover, in the
same spirit as the notion of KAM stable integrable Hamiltonians, we will introduce a notion of effectively stable integrable
Hamiltonians, conjecture a characterization of these Hamiltonians and show that our result proves this conjecture in the linear
case. |