Generic point equivalence and Pisot numbers

Let $\unicode[STIX]{x1D6FD}>1$ be an integer or, generally, a Pisot number. Put $T(x)=\{\unicode[STIX]{x1D6FD}x\}$ on $[0,1]$ and let $S:[0,1]\rightarrow [0,1]$ be a piecewise linear transformation whose slopes have the form $\pm \unicode[STIX]{x1D6FD}^{m}$ with positive integers $m$. We give a s...

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 40; no. 12; pp. 3169 - 3180
Main Authors AKIYAMA, SHIGEKI, KANEKO, HAJIME, KIM, DONG HAN
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2020
Subjects
Linear transformations
Numbers
Original Article
beta expansion
11K16
Pisot number
generic point
37E05
normal number
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Summary:Let $\unicode[STIX]{x1D6FD}>1$ be an integer or, generally, a Pisot number. Put $T(x)=\{\unicode[STIX]{x1D6FD}x\}$ on $[0,1]$ and let $S:[0,1]\rightarrow [0,1]$ be a piecewise linear transformation whose slopes have the form $\pm \unicode[STIX]{x1D6FD}^{m}$ with positive integers $m$. We give a sufficient condition for $T$ and $S$ to have the same generic points. We also give an uncountable family of maps which share the same set of generic points.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2019.46