On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus

• Date: 2002
• Main Authors: Kulik, V. L., Stepanenko, N. V., Кулик, В. Л., Степаненко, Н. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4094
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate the problem of the existence of the Green–Samoilenko function for linear expansions of dynamical systems on a torus of the form $$\frac{{d\phi }}{{dt}} = a(\phi ),{\text{ }}C(\phi )\frac{{d\phi }}{{dt}} + \frac{1}{2}\dot C(\phi )x = A(\phi )x,$$ where C(ϕ) ∈ C′(T m; a) is a nondeg...