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- W1548243771 abstract "We study a family of piecewise expanding maps on the plane, generated by composition of a rotation and an expansive similitude of expansion constant $beta$. We give two constants $B_1$ and $B_2$ depending only on the fundamental domain that if $beta>B_1$ then the expanding map has a unique absolutely continuous invariant probability measure, and if $beta>B_2$ then it is equivalent to $2$-dimensional Lebesgue measure. Restricting to a rotation generated by $q$-th root of unity $zeta$ with all parameters in $mathbb{Q}(zeta,beta)$, it gives a sofic system when $cos(2pi/q) in mathbb{Q}(beta)$ and $beta$ is a Pisot number. It is also shown that the condition $cos(2pi/q) in mathbb{Q}(beta)$ is necessary by giving a family of non-sofic systems for $q=5$." @default.
- W1548243771 created "2016-06-24" @default.
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- W1548243771 date "2015-02-05" @default.
- W1548243771 modified "2023-09-27" @default.
- W1548243771 title "Rotational beta expansion: Ergodicity and Soficness" @default.
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- W1548243771 doi "https://doi.org/10.48550/arxiv.1502.01793" @default.
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