On Some Properties of the Behavior of Linear Extensions of Dynamical Systems on a Torus under Perturbation of Phase Variables

Abstract

We investigate classes of linear extensions of dynamical systems on a torus for which the Lyapunov functions exist for an arbitrary flow on the torus. Linear extensions for which the Lyapunov functions exist only with varying coefficients are considered separately. We investigate the problem of preservation of regularity under perturbation of phase variables.