Construction of an infinite-dimensional invariant torus of a countable system of linear differential-difference equations by the method of its reduction in the angular variable

Abstract

We use the method of reduction in the angular variable to construct an infinite-dimensional invariant torus for a linear system of differential-difference equations that depends on an infinite set of constant deviations of arguments of different signs. This means that the function that defines the torus is represented in the form of the limit of a sequence of functions, each of which defines an invariant torus for the initial system reduced in the angular variable, as the order of reduction tends to infinity.