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arXiv · 2409.05822

Ergodicity and Algebraticity of the Fast and Slow Triangle Maps

Thomas Garrity·Jacob Lehmann Duke
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Abstract

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.

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Thomas Garrity, Jacob Lehmann Duke. 2024-09-22. Ergodicity and Algebraticity of the Fast and Slow Triangle Maps. https://arxiv.org/abs/2409.05822

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