A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus

Abstract

Under the assumption that a linear homogeneous system defined on the direct product of a torus and a Euclidean space is exponentially dichotomous on the semiaxes, we obtain a condition for the existence of a unique Green–Samoilenko function for the problem of invariant torus. We find an expression for this function in terms of projectors that determine the dichotomy on the semiaxes.