Uniform entropy vs topological entropy

• Autorzy: Dikran Dikranjan , Hans-Peter A. Kunzi
• Języki publikacji: EN

Abstrakty

EN

We discuss the connection between the topological entropy and the uniform entropy and answer several open questions from [10, 15]. We also correct several erroneous statements given in [10, 18] without proof.

Słowa kluczowe

EN

uniform spaces; topological entropy; uniform entropy

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-09-20

zaakceptowano

2015-01-15

online

2015-12-18

Twórcy

autor

Dikran Dikranjan

• Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy

autor

Hans-Peter A. Kunzi

• Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701,
  South Africa

Bibliografia

• [1] R.L. Adler, A. G. Konheim, and M. H. McAndrew, Topological entropy, Trans. Amer. Math. 114 (1965), 309–319.
• [2] D. Alcaraz, Recurrencia en sistemas dinámicos linealmente ordenados, extensiones y entropía de Bowen, Ph. D. Dissertion, Universitat Jaume I, 2001.
• [3] D. Alcaraz, D. Dikranjan and M. Sanchis, Infinitude of Bowen’s entropy for groups endomorphisms, in: Juan Carlos Ferrando andManolo López Pellicer, eds, Proceeding from the first Meeting in Topology and Functional Analysis, in Elce, Spain (2013), dedicated to J. Kakol’s 60-th birthday, Springer Verlag 2014, pp. 139–158.
• [4] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971) 401–414.
• [5] R. Bowen, Erratum to “Entropy for group endomorphisms and homogeneous spaces”, Trans. Amer. Math. Soc. 181 (1973) 509–510.
• [6] G. C. L. Brümmer, D. Dikranjan and H.-P. Künzi, Further properties of topological entropy and its connection to quasi uniform entropy, work in progress.
• [7] G. C. L. Brümmer, A. Hager, Functorial uniformization of topological spaces, Topology Appl. 27 (2) (1987) 113–127. [Crossref]
• [8] D. Dikranjan, A. Giordano Bruno, The Pinsker subgroup of an algebraic flow, Jour Pure Appl. Algebra, 216 (2012) 364–376. [WoS]
• [9] D. Dikranjan, A. Giordano Bruno, Limit free computation of entropy, Rendiconti istit. Mar. Univ. Trieste 44 (2012), 1–16.
• [10] D. Dikranjan and A. Giordano Bruno, Topological and algebraic entropy on groups, Arhangel0skii A. V., Moiz ud Din Khan; Kocinac L., ed., Proceedings Islamabad ICTA 2011, Cambridge Scientific Publishers (2012) 133–214.
• [11] D. Dikranjan, A. Giordano Bruno, The connection between topological and algebraic entropy, Topology Appl., 159, Issue 13 (2012), 2980–2989. [WoS]
• [12] D. Dikranjan, A. Giordano Bruno, Entropy in a category, ACS, Volume 21, Issue 1 (2013), Page 67–101.
• [13] D. Dikranjan, A. Giordano Bruno, Discrete dynamical systems in group theory, Note Mat. 33 (2013), no. 1, 1–48.
• [14] D. Dikranjan, A. Giordano Bruno, A uniform approach to chaos, work in progress.
• [15] D. Dikranjan, M. Sanchis, S. Virili, New and old facts about entropy in uniform spaces and topological groups, Topology Appl. 159 (2012) 1916–1942 [WoS]
• [16] A. Fedeli, On two notions of topological entropy for noncompact spaces, Chaos, Solitons and Fractals 40 (2009) 432–435. [Crossref][WoS]
• [17] L. Gillman and L. Jerrison, Rings of continuous functions, Graduate Texts in Mathematics, no. 43. Springer-Verlag, New York- Heidelberg, 1976
• [18] J. Hofer, Topological entropy for non-compact spaces, Michigan J. Math. 21 (1974) 235–242.
• [19] B.M. Hood, Topological entropy and uniform spaces, J. London Math. Soc. (2) (8) (1974), 633–641. [Crossref]
• [20] Takashi Kimura, Completion theorem for uniform entropy, Comment. Math. Univ. Carolin. 39 (1998), no. 2, 389–399.
• [21] E. Michael, Gg sections and compact-covering maps, Duke Math. J. 36 1969 125-127. [Crossref]

Identyfikatory

DOI

10.1515/taa-2015-0009