Multifractal analysis of the divergence points of Birkhoff averages in $beta$-dynamical systems

Yuanhong Chen, Zhenliang Zhang, Xiaojun Zhao

This paper is aimed at a detailed study of the multifractal analysis of the so-called divergence points in the system of $\beta$-expansions. More precisely, let $([0,1),T_{\beta })$ be the $β…