Remarks on uniform recurrence properties for beta-transformation

TL;DR

This paper discusses the uniform recurrence properties of points under beta-transformations, building on recent work by Zheng and Wu, with a focus on metrical aspects of orbit behavior.

Contribution

It provides additional insights or results regarding the uniform recurrence properties in beta-transformations, complementing prior research.

Findings

Enhanced understanding of recurrence behavior in beta-transformations

New metrical results on orbit uniform recurrence

Extensions or refinements of Zheng and Wu's findings

Abstract

We complement the recent paper of Zheng and Wu [Uniform recurrence properties for beta-transformation, Nonlinearity 33 (2020), 4590--4612], where the authors study, from the metrical point of view, the uniform recurrence properties of the orbit of a point under the $\beta$-transformation to the point itself.