Generic point equivalence and Pisot numbers

• Published in: Ergodic theory and dynamical systems Vol. 40; no. 12; pp. 3169 - 3180
• Main Authors: AKIYAMA, SHIGEKI, KANEKO, HAJIME, KIM, DONG HAN
• Format: Journal Article
• Language: English
• 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

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...