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A note on the periodic orbits and topological entropy of graph maps

Authors: Ll. Alsedà, D. Juher and P. Mumbrú
Journal: Proc. Amer. Math. Soc. 129 (2001), 2941-2946
MSC (2000): Primary 37E25, 37B40; Secondary 54H20, 54C70
Published electronically: April 17, 2001
MathSciNet review: 1840097
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This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

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Additional Information

Ll. Alsedà
Affiliation: Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08913 Cerdanyola del Vallès, Barcelona, Spain

D. Juher
Affiliation: Departament d’Informàtica i Matemàtica Aplicada, Universitat de Girona, Lluís Santaló s/n, 17071 Girona, Spain

P. Mumbrú
Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain

Keywords: Graph maps, periodic orbits, topological entropy
Received by editor(s): February 10, 2000
Published electronically: April 17, 2001
Additional Notes: The authors have been partially supported by the DGES grant number PB96-1153 and the INTAS OPEN 97 grant number 97-1843.
Communicated by: Michael Handel
Article copyright: © Copyright 2001 American Mathematical Society

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