Multifractal aspects of $\alpha$-expansions

Abstract

In \cite{[NE]} we introduce $\alpha$-expansions a real numbers in $(0,1]$, given by \[ \sum_{i=1}^{\infty}(α-1)^{i-1}α^{-(d_{1}+\dots+d_{i})}\] with $\alpha >1$ and $d_i\in \mathbb{N}$ and discuss ergodic theoretical and dimension theoretical aspects of this expansions. In this sequel we study mutifractal aspects of this expansions.