A new family of expansions of real numbers
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914835577438208 |
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| author | Neunhäuserer, Jörg |
| author_facet | Neunhäuserer, Jörg |
| contents | For $α>1$ we represent a real number in $(0,1]$ in the form \[ \sum_{i=1}^{\infty}(α-1)^{i-1}α^{-(d_{1}+\dots+d_{i})}\] with $d_{i}\in\mathbb{N}$. We discuss ergodic theoretical and dimension theoretical aspects of this expansion. Furthermore we study their base-change-transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new family of expansions of real numbers Neunhäuserer, Jörg Dynamical Systems Number Theory 11K55, 37A44, 28A80, 26A30 For $α>1$ we represent a real number in $(0,1]$ in the form \[ \sum_{i=1}^{\infty}(α-1)^{i-1}α^{-(d_{1}+\dots+d_{i})}\] with $d_{i}\in\mathbb{N}$. We discuss ergodic theoretical and dimension theoretical aspects of this expansion. Furthermore we study their base-change-transformation. |
| title | A new family of expansions of real numbers |
| topic | Dynamical Systems Number Theory 11K55, 37A44, 28A80, 26A30 |
| url | https://arxiv.org/abs/2406.10919 |