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On Extensions over Semigroups and Applications

Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
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Academic Editor: Tomasz Downarowicz
Entropy 2016, 18(6), 230; https://doi.org/10.3390/e18060230
Received: 22 April 2016 / Revised: 4 June 2016 / Accepted: 9 June 2016 / Published: 15 June 2016
(This article belongs to the Special Issue Entropic Properties of Dynamical Systems)
Applying a theorem according to Rhemtulla and Formanek, we partially solve an open problem raised by Hochman with an affirmative answer. Namely, we show that if G is a countable torsion-free locally nilpotent group that acts by homeomorphisms on X, and S G is a subsemigroup not containing the unit of G such that f 1 , s f : s S for every f C ( X ) , then ( X , G ) has zero topological entropy. View Full-Text
Keywords: extensions over semigroups; algebraic past; topological predictability; zero entropy extensions over semigroups; algebraic past; topological predictability; zero entropy
MDPI and ACS Style

Huang, W.; Jin, L.; Ye, X. On Extensions over Semigroups and Applications. Entropy 2016, 18, 230.

AMA Style

Huang W, Jin L, Ye X. On Extensions over Semigroups and Applications. Entropy. 2016; 18(6):230.

Chicago/Turabian Style

Huang, Wen; Jin, Lei; Ye, Xiangdong. 2016. "On Extensions over Semigroups and Applications" Entropy 18, no. 6: 230.

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