Generalized Discrete Nonlinear Schrödinger as a Normal Form at the Thermodynamic Limit for the Klein–Gordon Chain

A still open challenge in Hamiltonian dynamics is the development of a perturbation theory for Hamiltonian systems with an arbitrarily large number of degrees of freedom and, in particular, in the thermodynamic limit. Indeed, motivated by the problems arising in the foundations of Statistical Mechanics, it is relevant to consider large systems (e.g., for a model of a crystal the number of particles should be of the order of the Avogadro number) with non vanishing energy per particle (which corresponds to a non zero temperature in the physical model).