Rotation sets for graph maps of degree 1
de l'Institut Fourier, 58, No. 4, 1233-1294, 2008.
For a continuous map on a topological graph containing a loop S it
is possible to define the degree (with respect to the loop S) and,
for a map of degree 1, rotation numbers. We study the rotation set
of these maps and the periods of periodic points having a given
rotation number. We show that, if the graph has a single loop S then
the set of rotation numbers of points in S has some properties
similar to the rotation set of a circle map; in particular it is a
compact interval and for every rational \alpha in this interval
there exists a periodic point of rotation number \alpha.
For a special class of maps called combed maps, the rotation set
displays the same nice properties as the continuous degree one circle
[pdf (published paper)]