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Generic point equivalence and Pisot numbers

  • SHIGEKI AKIYAMA (a1), HAJIME KANEKO (a1) and DONG HAN KIM (a2)

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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Generic point equivalence and Pisot numbers

  • SHIGEKI AKIYAMA (a1), HAJIME KANEKO (a1) and DONG HAN KIM (a2)

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