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Tytuł artykułu

Uniform entropy vs topological entropy

Treść / Zawartość
Warianty tytułu
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
Wydawca
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2014-09-20
zaakceptowano
2015-01-15
online
2015-12-18
Twórcy
  • Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy
  • 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 FerrandoandManolo 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 uniformentropy, 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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_taa-2015-0009
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