Generic point equivalence and Pisot numbers

Abstract

Let $\beta >1$ be an integer or generally a Pisot number. Put $T(x)=\{\beta x\}$ on $[0,1]$ and let $S:[0,1]\to [0,1]$ be a piecewise linear transformation whose slopes have the form $\pm {\beta }^m$ with positive integers $m$. We give sufficient conditions that $T$ and $S$ have the same generic points.

12 pages