Kinetic theory and ergodic properties

It is often assumed that the justification of kinetic theory lies in ergodic theory. From the properties of the collision operator, which plays a basic role in our kinetic description of dynamical systems, we show that this is not the case. We deduce that the asymptotic behavior of a class of states and observables is determined by the collisional invariants, independently of the ergodicity of the system. The relation between our conclusion and the stability concepts for classical Hamiltonian systems, introduced by Moser and others, is briefly indicated.