On the set of periods for σ maps

Let a be the topological graph shaped like the letter σ. We denote by 0 the unique branching point of σ, and by O and I the closures of the components of homeomorphics to the circle and the interval, respectively. A continuous map from a into itself satisfying that f has a fixed point in O, or f has a fixed point and is called a a map. These are the continuous self-maps of a whose sets of periods can be studied without the notion of rotation interval. We characterize the sets of periods of all a maps. © 1995 American Mathematical Society. © 1995 American Mathematical Society.