The Hausdorff dimension of the region of multiplicity one of overlapping iterated function systems on the interval (Q2046770)

Consider the iterated function system \(T_{0}x=ax\), \(T_{1}x=ax+(1-a)\) for \(a>1/2\). The author studies the set \(U_{a}\) of those \(x\in[0,1]\) which have a unique address with respect to this IFS. If \(a\ge g\) it is well known that \(U_{a}=\{0,1\}\), where \(g\) is the golden ratio. In the paper under review the Hausdorff dimension of \(U_{a}\) is calculated for \(a\) in some intervals contained in \([1/2,g]\). The calculations use graph directed Markov systems, see [\textit{R. D. Mauldin} and \textit{M. Urbański}, Graph directed Markov systems. Geometry and dynamics of limit sets. Cambridge: Cambridge University Press (2003; Zbl 1033.37025)].