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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.08532 |
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Table of 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 $β$.