Exchange of Intervals and Intrinsic Ergodicity of the Negative Beta shift
Dynamical Systems
2026-05-15 v4
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.
Cite
@article{arxiv.2503.06597,
title = {Exchange of Intervals and Intrinsic Ergodicity of the Negative Beta shift},
author = {Florent Nguema Ndong and Anne Bertrand-Mathis},
journal= {arXiv preprint arXiv:2503.06597},
year = {2026}
}