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arXiv · 1905.03961

Generic point equivalence and Pisot numbers

Shigeki Akiyama·Hajime Kaneko·Dong Han Kim
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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.

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Shigeki Akiyama, Hajime Kaneko, Dong Han Kim. 2019-05-10. Generic point equivalence and Pisot numbers. https://doi.org/10.1017/etds.2019.46

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