Remarks on uniform recurrence properties for beta-transformation

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 ${\hat{I}}^2$-transformation to the point itself.

8 pages