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arXiv · 2503.06597

Exchange of Intervals and Intrinsic Ergodicity of the Negative Beta shift

Florent Nguema Ndong·Anne Bertrand-Mathis
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Abstract

This work highlights a peculiar phenomenon of interval exchange. Considering a real number beta less than -1, the negative beta-shift is coded if and only if its absolute value is greater than the golden ratio. We study an increasing sequence of algebraic integers with limit-1 and the absolute value of the first term equals to the golden ratio such that for a base x taken in the interval of consicutive terms of this sequence, the measure of the maximal entropy is carried by the image of a beta-shift, with the golden ratio les than the absolute value of beta, under the mapping of an injective substitution.

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Florent Nguema Ndong, Anne Bertrand-Mathis. 2025-03-09. Exchange of Intervals and Intrinsic Ergodicity of the Negative Beta shift. https://arxiv.org/abs/2503.06597

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