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arXiv · 1810.11135

Intrinsic ergodicity for factors of $(-\beta)$-shifts

Mao Shinoda·Kenichiro Yamamoto
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Abstract

We show that every subshift factor of a ($-\beta$)-shift is intrinsically ergodic, when $\beta\geq \frac{1+\sqrt{5}}{2}$ and the ($-\beta$)-expansion of $1$ is not periodic with odd period. Moreover, the unique measure of maximal entropy satisfies a certain Gibbs property. This is an application of the technique established by Climenhaga and Thompson to prove intrinsic ergodicity beyond specification. We also prove that there exists a subshift factor of a ($-\beta$)-shift which is not intrinsically ergodic in the cases other than the above.

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Mao Shinoda, Kenichiro Yamamoto. 2018-10-25. Intrinsic ergodicity for factors of $(-\beta)$-shifts. https://arxiv.org/abs/1810.11135

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