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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Entropy and periodic points for transitive maps


Authors: Ll. Alsedà, S. Kolyada, J. Llibre and L. Snoha
Journal: Trans. Amer. Math. Soc. 351 (1999), 1551-1573
MSC (1991): Primary 58F11, 34C35, 54H20
MathSciNet review: 1451592
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Abstract: The aim of this paper is to investigate the connection between transitivity, density of the set of periodic points and topological entropy for low dimensional continuous maps. The paper deals with this problem in the case of the $n$-star and the circle among the one-dimensional spaces and in some higher dimensional spaces. Particular attention is paid to triangular maps and to extensions of transitive maps to higher dimensions without increasing topological entropy.


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Additional Information

Ll. Alsedà
Affiliation: Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08193 – Bellaterra, Barcelona, Spain
Email: alseda@mat.uab.es

S. Kolyada
Affiliation: Institute of Mathematics, Ukrainian Academy of Sciences, Tereshchenkivs’ka 3, 252601 Kiev – 4, Ukraine
Email: skolyada@math.carrier.kiev.ua

J. Llibre
Affiliation: Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08193 – Bellaterra, Barcelona, Spain
Email: jllibre@mat.uab.es

L. Snoha
Affiliation: Department of Mathematics, FPV, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
Email: snoha@bb.sanet.sk

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02077-2
PII: S 0002-9947(99)02077-2
Keywords: Transitive maps, topological entropy, periodic points, triangular maps
Received by editor(s): September 20, 1995
Received by editor(s) in revised form: November 26, 1996
Dedicated: Dedicated to the memory of Wiesław Szlenk
Article copyright: © Copyright 1999 American Mathematical Society