多维高斯映射

摘要：

经典的高斯映射是从单位区间到自身的分段连续映射。从这个映射中我们得到了无理数的连分数展开式及其动力学性质，给出了无理数的一些算术和代数性质的信息。在本笔记中，我们将探索高斯映射到更高维度的一些推广，并提出一些关于这些映射可能携带的算术/代数信息的问题和说明。

英文摘要：

The classical Gauss Map is a piecewise continuous map from the unit interval to itself. From this map we retrieve the continued fraction expansion of irrational numbers and its dynamical properties give information about some arithmetic and algebraic properties of irrational numbers. In this notes we will explore some generalizations of the Gauss Map to higher dimensions and pose some questions and conjectures about the arithmetic/algebraic information that these maps may carry.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。