Orbit types and minimal dynamics for graph maps

Ll Alsedà, Francois Gautero, J. Guaschi, J. Los, F. Mañosas, P. Mumbrú

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

We define the type of a periodic orbit of a graph map. We consider the class of 'train-track' representatives, that is, those graph maps which minimise the topological entropy of the topological representatives of a given free group endomorphism. We prove that each type of periodic orbit realised by an efficient representative is also realised by any representative of the same free group endomorphism. Moreover, the number of periodic orbits of a given type is minimised by the efficient representatives. © 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.
Original languageEnglish
Pages (from-to)479-482
JournalComptes Rendus Mathematique
Volume334
DOIs
Publication statusPublished - 30 Mar 2002

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