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Entropy 2016, 18(6), 230; doi:10.3390/e18060230

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
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)
View Full-Text   |   Download PDF [222 KB, uploaded 15 June 2016]

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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

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