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Generic point equivalence and Pisot numbers
Published online by Cambridge University Press: 11 July 2019
Abstract
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.
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- © Cambridge University Press, 2019