Rotation sets for graph maps of degree 1

Lluís Alsedà, Sylvie Ruette

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7 Citations (Scopus)


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 α in this interval there exists a periodic point of rotation number α. For a special class of maps called combed maps, the rotation set displays the same nice properties as the continuous degree one circle maps.
Original languageEnglish
Pages (from-to)1233-1294
JournalAnnales de l'Institut Fourier
Issue number4
Publication statusPublished - 1 Jan 2008


  • Graph maps
  • Rotation numbers
  • Sets of periods


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