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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
Posted:
April 17, 2001
MathSciNet review:
1840097
Full-text PDF Free Access
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Additional Information
Abstract: 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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- Ll. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and entropy in dimension one, Advanced Series in Nonlinear Dynamics 5, World Scientific, Singapore, 1993. MR 95j:58042
- 3.
- Ll. Alsedà, F. Mañosas and P. Mumbrú, Minimizing topological entropy for continuous maps on graphs, Ergod. Th. & Dynam. Sys. 20 (2000), 1559-1576. CMP 2001:06
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- S. Baldwin and E. Slaminka, Calculating topological entropy, J. Stat. Phys. 89 (1997), 1017-1033. MR 99a:58100
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- M. Misiurewicz and Z. Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 94, no. 456 (1991). MR 92h:58105
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- Y. Takahashi, A formula for topological entropy of one-dimensional dynamics, Sci. Papers College Gen. Ed. Univ. Tokyo 30 (1980), 11-22. MR 82i:58057
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Additional Information
Ll. Alsedà
Affiliation:
Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08913 Cerdanyola del Vallès, Barcelona, Spain
Email:
alseda@mat.uab.es
D. Juher
Affiliation:
Departament d’Informàtica i Matemàtica Aplicada, Universitat de Girona, Lluís Santaló s/n, 17071 Girona, Spain
Email:
juher@ima.udg.es
P. Mumbrú
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
Email:
mumbru@mat.ub.es
DOI:
http://dx.doi.org/10.1090/S0002-9939-01-06134-2
PII:
S 0002-9939(01)06134-2
Keywords:
Graph maps,
periodic orbits,
topological entropy
Received by editor(s):
February 10, 2000
Posted:
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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