A characterization of the set Ω(f) \ ω(f) for continuous maps of the interval with zero topological entropy

Abstract

We give a characterization of the set of nonwandering points of a continuous map \(f\) of the interval with zero topological entropy, attracted to a single (infinite) minimal set \(Q\). We show that such a map \(f\) can have a unique infinite minimal set \(Q\) and an infinite set \(B\subset\Omega (f)\setminus\omega (f)\) (of nonwandering points that are not \(\omega\)-limit points) attracted to \(Q\) and such that \(B\) has infinite intersections with infinitely many disjoint orbits of \(f\).