Abstract

For a continuous map on a topological graph containing a loop it is possible to define the degree (with respect to that loop) and, for a map of degree 1, the rotation numbers. We study the rotation set and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop then the set of rotation numbers of points in the loop has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational $p/q$ in this interval there exists a periodic point of rotation number $p/q$ (but not necessarily of period $q$).
Joint work with Sylvie Ruette.