Sources, sinks and saddles for expansive homeomorphism with canonical coordinates
Let f be an expansive self-homeomorphism of a compact metric space X and assume that f has canonical coordinates. Since the coordinates change with the movement of a point certain properties of fixed points may be studied for any point. The authors generalize the notions of a source, sink and saddle to any point of X. According to a primary theorem of the paper, if X is compact, connected and locally connected and f is expansive self-homeomorphism of X with canonical coordinates, then X consists of just one point or else every point of X is a saddle point. By means of an example, they show that the condition of local connectedness may not be omitted from the hypotheses.
scientific article; zbMATH DE number 4040817