On the stability of an invariant torus - Dudzyanyi, S. I.; Perestyuk, N. A. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
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.