Exchange of Intervals and Intrinsic Ergodicity of the Negative Beta shift
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913124744953856 |
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| author | Ndong, Florent Nguema Bertrand-Mathis, Anne |
| author_facet | Ndong, Florent Nguema Bertrand-Mathis, Anne |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06597 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exchange of Intervals and Intrinsic Ergodicity of the Negative Beta shift Ndong, Florent Nguema Bertrand-Mathis, Anne Dynamical Systems 11K16, 11B05, 37A05, 37A25, 37B10 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. |
| title | Exchange of Intervals and Intrinsic Ergodicity of the Negative Beta shift |
| topic | Dynamical Systems 11K16, 11B05, 37A05, 37A25, 37B10 |
| url | https://arxiv.org/abs/2503.06597 |