Generic point equivalence and Pisot numbers

Shigeki Akiyama, Hajime Kaneko, Dong Han Kim

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 $\…