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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05822 |
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| _version_ | 1866910615647289344 |
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| author | Garrity, Thomas Duke, Jacob Lehmann |
| author_facet | Garrity, Thomas Duke, Jacob Lehmann |
| contents | Our goal is to show that both the fast and slow versions of the triangle map (a type of multi-dimensional continued fraction algorithm) in dimension $n$ are ergodic, resolving a conjecture of Messaoudi, Noguiera and Schweiger. This particular type of higher dimensional multi-dimensional continued fraction algorithm has recently been linked to the study of partition numbers, with the result that the underlying dynamics has combinatorial implications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05822 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ergodicity and Algebraticity of the Fast and Slow Triangle Maps Garrity, Thomas Duke, Jacob Lehmann Dynamical Systems Number Theory 11K55, 11J70, 11R04, 28D99 Our goal is to show that both the fast and slow versions of the triangle map (a type of multi-dimensional continued fraction algorithm) in dimension $n$ are ergodic, resolving a conjecture of Messaoudi, Noguiera and Schweiger. This particular type of higher dimensional multi-dimensional continued fraction algorithm has recently been linked to the study of partition numbers, with the result that the underlying dynamics has combinatorial implications. |
| title | Ergodicity and Algebraticity of the Fast and Slow Triangle Maps |
| topic | Dynamical Systems Number Theory 11K55, 11J70, 11R04, 28D99 |
| url | https://arxiv.org/abs/2409.05822 |