The reduction principle for discrete dynamical and semidynamical systems in metric spaces

The main result of this paper is on decoupling by means of a topological transformation of a homeomorphism which admits invariant sets. A theorem of conjugacy of a given possible noninvertible mapping, which admits an invariant set, to a simpler mapping than the given one in terms of decoupling is also proved. The results are valid in an arbitrary complete metric space.This work has been completed with the financial support of Latvian Council of Science under Grants 90.224 and 93.809.