Limit Sets and Prolongations in Generalized (Multivalued) Semi-Systems

摘要

The paper contains a review of some recent results concerning limit sets,prolongations and prolongational limit sets in generalized ('multivalued') semi-systems on metric spaces. These sets are defined in a 'sequential' form, which is suitable for Hausdorff topological spaces fulfilling the first countability axiom (and so, in particular, for metric spaces). The definitions are direct and natural extensions of the classical ones, taken from the theory of dynamical systems and semi-systems on metric spaces.