Introduction:
The study of Hamiltonian systems is of relevant interest for Physics.
These may consist of classical systems, namely with a finite number of degrees of freedom, like the Nbody problem, the planetary problem, the rigid body, billiards, the spinorbit system, or, more generally, of “extended systems”, with a infinite number of degrees of freedom, like, for example, the Schrödinger equation, the wave equation, the Euler equations of hydrodynamics.
Since the early 50s, many robust techniques have been applied firstly to classical and next also to extended systems, like the theorem of Kolmogorov, Moser and Arnold, the theorem of Nekhorossev, Arnold’s instability for systems with more than two degrees of freedom, splitting of separatrices, variational techniques, Mather theory.
In this special session, we aim to gather specialist in this field, to outline the “status of the art” and perspectives. 
