ON SET-VALUED DISCRETE DYNAMICAL SYSTEMS.

In this paper, we attempt to study set-valued discrete dynamical systems with the objective of developing a general framework and unifying some results and definitions in the literature. For these purposes, we follow similar ideas to those existing for classical dynamical systems. We focus on discrete dynamical systems in terms of set-valued maps. The solutions associated to our systems are given by sequences of sets. We obtain preliminary results by formulating appropriate notions of set dynamical systems as attractor, stability and invariant sets. For this purpose, we study the ω-limit sets which play an important role for gaining an overall understanding of how the system is behaving, particularly in the long term. We study its properties by using well-known notions from set-valued analysis. We are able to generalize dynamical results in terms of single valued maps by the weaker assumptions on continuity. [ABSTRACT FROM AUTHOR]