Stabilisability and beta representations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914031378366464 |
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| author | Dettmann, Carl P. |
| author_facet | Dettmann, Carl P. |
| contents | We consider a one dimensional affine switched system obtained from a formal limit of a two dimensional linear system. We show this is equivalent to minimising the average digit in beta representations with unrestricted digits. We give a countable set of $β$ for which the result is given by the usual (greedy) beta expansion, an interval of values for which it is strictly less, and a conditional lower bound for all $β$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilisability and beta representations Dettmann, Carl P. Optimization and Control Dynamical Systems We consider a one dimensional affine switched system obtained from a formal limit of a two dimensional linear system. We show this is equivalent to minimising the average digit in beta representations with unrestricted digits. We give a countable set of $β$ for which the result is given by the usual (greedy) beta expansion, an interval of values for which it is strictly less, and a conditional lower bound for all $β$. |
| title | Stabilisability and beta representations |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2509.08532 |