Uniform entropy vs topological entropy

Dikran Dikranjan; Hans-Peter A. Kunzi

Topological Algebra and its Applications (2015)

  • Volume: 3, Issue: 1
  • ISSN: 2299-3231

Abstract

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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.

How to cite

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Dikran Dikranjan, and Hans-Peter A. Kunzi. "Uniform entropy vs topological entropy." Topological Algebra and its Applications 3.1 (2015): null. <http://eudml.org/doc/276420>.

@article{DikranDikranjan2015,
abstract = {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.},
author = {Dikran Dikranjan, Hans-Peter A. Kunzi},
journal = {Topological Algebra and its Applications},
keywords = {uniform spaces; topological entropy; uniform entropy},
language = {eng},
number = {1},
pages = {null},
title = {Uniform entropy vs topological entropy},
url = {http://eudml.org/doc/276420},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Dikran Dikranjan
AU - Hans-Peter A. Kunzi
TI - Uniform entropy vs topological entropy
JO - Topological Algebra and its Applications
PY - 2015
VL - 3
IS - 1
SP - null
AB - 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.
LA - eng
KW - uniform spaces; topological entropy; uniform entropy
UR - http://eudml.org/doc/276420
ER -

References

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  1. [1] R.L. Adler, A. G. Konheim, and M. H. McAndrew, Topological entropy, Trans. Amer. Math. 114 (1965), 309–319. Zbl0127.13102
  2. [2] D. Alcaraz, Recurrencia en sistemas dinámicos linealmente ordenados, extensiones y entropía de Bowen, Ph. D. Dissertion, Universitat Jaume I, 2001. 
  3. [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. [4] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971) 401–414. Zbl0212.29201
  5. [5] R. Bowen, Erratum to “Entropy for group endomorphisms and homogeneous spaces”, Trans. Amer. Math. Soc. 181 (1973) 509–510. Zbl0275.22013
  6. [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. [7] G. C. L. Brümmer, A. Hager, Functorial uniformization of topological spaces, Topology Appl. 27 (2) (1987) 113–127. [Crossref] Zbl0639.54019
  8. [8] D. Dikranjan, A. Giordano Bruno, The Pinsker subgroup of an algebraic flow, Jour Pure Appl. Algebra, 216 (2012) 364–376. [WoS] Zbl1247.37014
  9. [9] D. Dikranjan, A. Giordano Bruno, Limit free computation of entropy, Rendiconti istit. Mar. Univ. Trieste 44 (2012), 1–16. 
  10. [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. Zbl1300.54002
  11. [11] D. Dikranjan, A. Giordano Bruno, The connection between topological and algebraic entropy, Topology Appl., 159, Issue 13 (2012), 2980–2989. [WoS] Zbl1256.54061
  12. [12] D. Dikranjan, A. Giordano Bruno, Entropy in a category, ACS, Volume 21, Issue 1 (2013), Page 67–101. Zbl1337.18005
  13. [13] D. Dikranjan, A. Giordano Bruno, Discrete dynamical systems in group theory, Note Mat. 33 (2013), no. 1, 1–48. Zbl1280.37023
  14. [14] D. Dikranjan, A. Giordano Bruno, A uniform approach to chaos, work in progress. 
  15. [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] Zbl1242.54005
  16. [16] A. Fedeli, On two notions of topological entropy for noncompact spaces, Chaos, Solitons and Fractals 40 (2009) 432–435. [Crossref][WoS] Zbl1197.37014
  17. [17] L. Gillman and L. Jerrison, Rings of continuous functions, Graduate Texts in Mathematics, no. 43. Springer-Verlag, New York- Heidelberg, 1976 
  18. [18] J. Hofer, Topological entropy for non-compact spaces, Michigan J. Math. 21 (1974) 235–242. Zbl0287.54044
  19. [19] B.M. Hood, Topological entropy and uniform spaces, J. London Math. Soc. (2) (8) (1974), 633–641. [Crossref] Zbl0291.54051
  20. [20] Takashi Kimura, Completion theorem for uniform entropy, Comment. Math. Univ. Carolin. 39 (1998), no. 2, 389–399. 
  21. [21] E. Michael, Gg sections and compact-covering maps, Duke Math. J. 36 1969 125-127. [Crossref] 

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