Chaos and order of inverse limit space for a graph map
The paper deals with several criteria of chaos for piecewise monotone continuous maps on finite graphs. Here, it is proved that a piecewise monotone continuous map of a finite graph is non-chaotic in the sense of Li-Yorke if and only if the order of the inverse limit space using the map as a sole bonding map. In other words, if the map is non-chaotic, then the topological structure of its inverse limit space is relatively simple, and vice versa. Moreover, he proves that a piecewise monotone continuous map of a finite graph is non-chaotic if and only if every point in the intersection of the set of recurrent points of the map and the closure of the set of periodic points is a regularly recurrent point.
scientific article; zbMATH DE number 1445758