Analogues of Jacobi and Weyl Theorems for Infinite-Dimensional Tori

The generalization of Jacobi and Weyl theorems on the dynamics of oscillators on an infinite dimensional tori is presented. As in the classical theorems by Jacibi and Weyl on the linear flow on a finite dimensional torus conditions are obtained for periodicity, nonwandering, ergodicity and transitivity on an invariant torus of trajectories of an infinite system of oscillators. We study the ergodicity of a measure on an invariant torus with respect to the flow of a system of oscillators.Comment: 13 pages, 0 figure