快慢三角映射的遍历性和代数性

arXiv - MATH - Number Theory Pub Date : 2024-09-09 DOI:arxiv-2409.05822

Thomas Garrity, Jacob Lehmann Duke

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引用次数: 0

摘要

我们的目标是证明三角形映射（一种多维连续分数算法）在 $n$ 维度下的快速和慢速版本都是连续的，从而解决 Messaoudi、Noguiera 和 Schweiger 的一个猜想。这种特殊类型的高维多维连续分数算法最近与分割数的研究联系在一起，其结果是基本动力学具有组合意义。

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Ergodicity and Algebraticity of the Fast and Slow Triangle Maps

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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arXiv - MATH - Number Theory

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