On the stability of an invariant torus

• Date: 1997
• Main Authors: Dudzyanyi, S. I., Perestyuk, N. A., Дудзяний, С. І., Перестюк, М. О.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1997
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5120
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the problem of the asymptotic stability for trivial invariant torus of a linear extension of dynamical system on a torus. We formulate and prove sufficient criteria of asymptotic stability and study conditions for the existence and uniqueness of the Lyapunov functions of fixed sign.