Involutive functionals, infinite dimensional tori, and neighboring tori (Q1270007)

In the space of smooth periodic functions of one variable, the author considers Hamiltonian equations of the form \(u_t=K(u)\), whose constants of motion \(F_m(u)\) are in involution. An infinite dimensional version of the Liouville theorem is obtained. The author discusses in what sense the generic level of the functionals \(F_m\) may be considered as an infinite dimensional torus, time almost periodicity of the solutions, and relations between generic neighboring tori.