A criterion for the existence of the unique invariant torus of a linear extension of dynamical systems - Boichuk, О. A. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
Under the assumption that a linear homogeneous system defined on the direct product of a torus and the Euclidean space is exponentially dichotomous on semiaxes, we obtain a necessary and sufficient condition for the existence of the unique invariant torus of the corresponding inhomogeneous linear system.