|
A note on the periodic orbits and topological entropy of graph maps
Author(s):
Ll.
Alsedà;
D.
Juher;
P.
Mumbrú
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2941-2946.
MSC (2000):
Primary 37E25, 37B40;
Secondary 54H20, 54C70
Posted:
April 17, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
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.
References:
-
- 1.
- R. Adler, A. Konheim and M. McAndrew, Topological entropy, Trans. Am. Math. Soc. 114 (1965), 309-319. MR 30:5291
- 2.
- 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
- 4.
- S. Baldwin and E. Slaminka, Calculating topological entropy, J. Stat. Phys. 89 (1997), 1017-1033. MR 99a:58100
- 5.
- L. Block and E. Coven, Approximating entropy of maps of the interval, Proceedings of the semester on Ergodic Theory and Dynamical Systems, 237-241, Banach Center Pub. 23, PWN, Warsaw, 1989. MR 92c:58106
- 6.
- R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Am. Math. Soc. 153 (1971), 401-414 MR 43:469; erratum: Trans. Am. Math. Soc. 181 (1973), 509-510. MR 47:8810
- 7.
- P. Góra and A. Boyarsky, Computing the topological entropy of general one-dimensional maps, Trans. Am. Math. Soc. 323 (1991), 39-49. MR 92a:58083
- 8.
- J. Llibre and M. Misiurewicz, Horseshoes, entropy and periods for graph maps, Topology 32 (1993), 649-664. MR 94k:58113
- 9.
- M. Misiurewicz and Z. Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 94, no. 456 (1991). MR 92h:58105
- 10.
- M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings, Studia Math. 67 (1980), 45-63. MR 82a:58030
- 11.
- S. Newhouse and T. Pignataro, On the estimation of topological entropy, J. Stat. Phys. 72 (1993), 1331-1351. MR 94i:58116
- 12.
- 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
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
37E25, 37B40,
54H20, 54C70
Retrieve articles in all Journals with MSC
(2000):
37E25, 37B40,
54H20, 54C70
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:
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
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org