Following Schweiger’s generalization of multidimensional continued fraction algorithms, we consider a very large family of $p$-adic multidimensional continued fraction algorithms, which include Schneider’s algorithm, Ruban’s algorithms, and the $p$-adic Jacobi–Perron algorithm as special cases. The main result is to show that all the transformations in the family are ergodic with respect to the Haar measure.

中文翻译：

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遍历为 $磷$-adic 连分数算法

遵循 Schweiger 对多维连分数算法的推广，我们考虑了一个非常大的家族 $磷$-adic 多维连分数算法，包括 Schneider 算法、Ruban 算法和 $磷$-adic Jacobi-Perron 算法作为特例。主要结果是表明，关于 Haar 测度，族中的所有变换都是遍历的。