General methods of componentwise asymptotic equivalence of difference-dynamical systems (DDS)

Abstract

In this paper considered the asymptotic equivalence of difference-dynamical systems (DDS) under certain restrictions. Equivalences of these restrictions were called componentwise asymptotically equivalent. The results for the partitioning of total DDS equivalence classes componentwise properties were received, in which the behavior of solutions at infinity in some sense homogeneous. The result is an analogue of Nemytsky’s work, which is called the equivalence Nemytsky for systems of differential equations. From this work there is a special case of asymptotic equivalence of the Lyapunov, Levinson, Brauer.