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Topological Entropy of Free Semigroup Actions(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2019年02期
Page:
61-64
Research Field:
·数学与计算机科学·
Publishing date:

Info

Title:
Topological Entropy of Free Semigroup Actions
Author(s):
Zhang Wenda1; Xue Licui2
(1.College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)(2.College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050024,China)
Keywords:
free semigroup action; separated set; spanning set; open cover; topological entropy; equitopological conjugate
PACS:
37A35,37B40
DOI:
10.3969/j.issn.1001-4616.2019.02.010
Abstract:
In this paper,we define the entropy and preimage entropy of free semigroup actions in a new method. Based on these definitions,we get some relations between topological entropy and measure entropy,and the relations among kinds of preimage entropies. The main results of this paper are as follows:(1)The topological entropy is invariant under equi-conjugacy;(2)The power rule for the measure-theoretic entropy holds.

References:

[1] DINABURG E I. The relation between topological entropy and metric entropy[J]. Soviet Math Dokl,1970,11:13-16.
[2]WALTERS P. An Introduction to Ergodic Theory[M]. New York,Heidel-Berg,Berlin:Springer-Verlag,1982.
[3]ADLER R,KONHEIM A,MCANDREW M. Topological entropy[J]. Trans Amer Math Soc,1965,114:303-319.
[4]BOWEN R. Entropy for group endomorphisms and homogeneous spaces[J]. Trans AMS,1971,181:509-510.
[5]KOLYADA S,SNOHA L. Topological entropy of nonautonomous dynamical systems[J]. Random and Compu Dynam,1996,4(2/3):205-223.
[6]KATOK A,HASSELBLATT B. Introduction to the modern theory of dynamical systems[M]. New York:Cambridge University Press,1995.
[7]RUELLE D. Statistical mechanics on a compact set with tion satisfying expansiveness and specication[J]. Trans Amer Math Soc,1973,185:237-251.
[8]FRIEDLAND S. Entropy of graphs,semi-groups and groups[M]//Schmidt M,Pollicott K. Ergodic theory of Zd-actions. London Math Soc Lecture Note Ser 228. Cambridge:Cambridge University Press,1996:319-343.
[9]GELLER W,POLLICOTT M. An entropy for Z2-actions with finite entropy generators[J]. Fund Math,1998,157:209-220.
[10]ZHU Y,ZHANG W. On an entropy of Zk+-actions[J]. Acta Math Sinica Chin Ser,2014,30:467-480.
[11]ZHANG W,ZHANG J. The upper bounds of Friedland’s entropy for certain Zk+-actions[J]. Dyn Syst,2014,29:67-77.

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Last Update: 2019-06-30