On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus - Kulik, V. L.; Stepanenko, N. V. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We investigate the problem of the existence of the Green–Samoilenko function for linear expansions of dynamical systems on a torus of the form $$\frac{{dφ }}{{dt}} = a(φ ),{\text{ }}C(φ )\frac{{dφ }}{{dt}} + \frac{1}{2}\dot C(φ )x = A(φ )x,$$ where C(ϕ) ∈ C′(T m; a) is a nondegenerate symmetric matrix.