THE STRUCTURE OF MINIMAL ATTRACTION CENTERS OF TRAJECTORIES OF CONTINUOUS MAPS OF THE INTERVAL

Abstract

The structure of minimal attraction centers of trajectories of continuous maps of the interval is investigated. It is proved that a closed subset $S$ of the interval is the minimal attraction center of a trajectory of a continuous map of the interval into itself if and only if $S$ is either a nowhere dense set or a union of finitely many mutually disjoint nondegenerate closed intervals.