Chaos and entropy for graph maps (Q1890472)

It is well known that for any continuous map of a compact interval into itself, its chaoticity in the sense of Devaney is equivalent to its positive entropy. This fact holds also for maps of the circle. The author generalizes these results to graph maps. The author shows that the notions of positive entropy, chaos in the sense of Devaney and \(\omega\)-chaos are equivalent for the graph maps.