Investigation of a discrete dynamical system in a neighborhood of the invariant torus

We study the behavior of a discrete dynamical system in a neighborhood of the invariant torus for the case where the trajectories may have arbitrary structure on the torus and establish conditions under which the system can be reduced to the canonical form in the indicated neighborhood.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1676–1685, December, 1995.