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arXiv · 2009.11041

Ergodicity for $p$-adic continued fraction algorithms

Hui Rao·Shin-ichi Yasutomi
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Abstract

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.

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Hui Rao, Shin-ichi Yasutomi. 2020-09-23. Ergodicity for $p$-adic continued fraction algorithms. https://arxiv.org/abs/2009.11041

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