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Entropy of $\text{AT}(n)$ systems

Published online by Cambridge University Press:  19 September 2016

RADU B. MUNTEANU
RADU B. MUNTEANU*
Affiliation:
Department of Mathematics, University of Bucharest, 14 Academiei St., 010014 Bucharest, Romania email radu-bogdan.munteanu@g.unibuc.ro
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Abstract

In this paper we show that any ergodic measure preserving transformation of a standard probability space which is $\text{AT}(n)$ for some positive integer $n$ has zero entropy. We show that for every positive integer $n$ any Bernoulli shift is not $\text{AT}(n)$. We also give an example of a transformation which has zero entropy but does not have property $\text{AT}(n)$ for any integer $n\geq 1$.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 3 , May 2018 , pp. 1118 - 1126
Copyright
© Cambridge University Press, 2016 

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