Entropy of $\text{AT}(n)$ systems
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 transf...
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Veröffentlicht in: | Ergodic theory and dynamical systems 2018-05, Vol.38 (3), p.1118-1126 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | 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
$n\geq 1$
. |
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ISSN: | 0143-3857 1469-4417 |
DOI: | 10.1017/etds.2016.52 |