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.
@article{bwmeta1.element.doi-10_1515_taa-2015-0009,
author = {Dikran Dikranjan and Hans-Peter A. Kunzi},
title = {Uniform entropy vs topological entropy},
journal = {Topological Algebra and its Applications},
volume = {3},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_taa-2015-0009}
}
Dikran Dikranjan; Hans-Peter A. Kunzi. Uniform entropy vs topological entropy. Topological Algebra and its Applications, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_taa-2015-0009/
[1] R.L. Adler, A. G. Konheim, and M. H. McAndrew, Topological entropy, Trans. Amer. Math. 114 (1965), 309–319. | Zbl 0127.13102
[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. | Zbl 0212.29201
[5] R. Bowen, Erratum to “Entropy for group endomorphisms and homogeneous spaces”, Trans. Amer. Math. Soc. 181 (1973) 509–510. | Zbl 0275.22013
[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] | Zbl 0639.54019
[8] D. Dikranjan, A. Giordano Bruno, The Pinsker subgroup of an algebraic flow, Jour Pure Appl. Algebra, 216 (2012) 364–376. [WoS] | Zbl 1247.37014
[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. | Zbl 1300.54002
[11] D. Dikranjan, A. Giordano Bruno, The connection between topological and algebraic entropy, Topology Appl., 159, Issue 13 (2012), 2980–2989. [WoS] | Zbl 1256.54061
[12] D. Dikranjan, A. Giordano Bruno, Entropy in a category, ACS, Volume 21, Issue 1 (2013), Page 67–101. | Zbl 1337.18005
[13] D. Dikranjan, A. Giordano Bruno, Discrete dynamical systems in group theory, Note Mat. 33 (2013), no. 1, 1–48. | Zbl 1280.37023
[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] | Zbl 1242.54005
[16] A. Fedeli, On two notions of topological entropy for noncompact spaces, Chaos, Solitons and Fractals 40 (2009) 432–435. [Crossref][WoS] | Zbl 1197.37014
[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. | Zbl 0287.54044
[19] B.M. Hood, Topological entropy and uniform spaces, J. London Math. Soc. (2) (8) (1974), 633–641. [Crossref] | Zbl 0291.54051
[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]