Resumen de Sets of All o-Limit Points for One-Dimensional Maps

Naotsugu Chinen

• Let f be a continuous map from a graph G to itself and m the maximum of orders of all points of G. The main result of this paper is that a point c in G lies in the limit set of some point of G if and only if every open neighborhood of c contains at least (m + 1) points of some trajectory. This shows that every set of all limit points for every graph map satisfies the analogue to the Birkhoff theorem. But, the above does not holds for one-dimensional maps.