The comitants of Lyapunov system with respect to the rotation group and applications

Abstract

We investigate the action of the rotation group SO(2, R) on the system. Following analogically were defined the comitants of differential systems with respect to the rotation group. The Lie operator of the representation of the group SO(2, R) in the space EN(x, y, A) of the system was defined. Using this Lie operator was determined the criterion when a polynomial is a comitant of Lyapunov system with respect to the rotation group.