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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Entropy and periodic points for transitive maps
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by Ll. Alsedà, S. Kolyada, J. Llibre and Ľ. Snoha PDF
Trans. Amer. Math. Soc. 351 (1999), 1551-1573 Request permission

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.
References
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Additional Information
  • Ll. Alsedà
  • Affiliation: Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08193 – Bellaterra, Barcelona, Spain
  • MR Author ID: 212847
  • Email: alseda@mat.uab.es
  • S. Kolyada
  • Affiliation: Institute of Mathematics, Ukrainian Academy of Sciences, Tereshchenkivs’ka 3, 252601 Kiev – 4, Ukraine
  • MR Author ID: 196872
  • 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
  • Ľ. Snoha
  • Affiliation: Department of Mathematics, FPV, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
  • Email: snoha@bb.sanet.sk
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1551-1573
  • MSC (1991): Primary 58F11, 34C35, 54H20
  • DOI: https://doi.org/10.1090/S0002-9947-99-02077-2
  • MathSciNet review: 1451592