# Rotation sets for graph maps of degree 1

*by Professor Lluis Alseda*

*Institution:*Departament de Matematiques, Universitat Autonoma de Barcelona

*Date: Fri 21st October 2005*

*Time: 3:15 PM*

*Location: Theatre 2, Ground Floor, ICT Building (111 Barry St, Carlton)*

*Abstract*: 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 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 $\alpha$.

Joint work with Lluis Alseda and Sylvie Ruette.

*For More Information:* Emma Lockwood tel. 8344-1617 email: e.lockwood@ms.unimelb.edu.au