Pausinger, Florian; Schmid, Wolfgang Ch. A lower bound for the diaphony of generalised van der Corput sequences in arbitrary base \(b\). (English) Zbl 1313.11096 Unif. Distrib. Theory 6, No. 2, 31-46 (2011). Let \(q\geq 2\) be an integer and, for \(0<c<1\), put \[ F_c^q=\{x\in [0,1)\:\{q^n x\}\geq c,\;\forall ~n\geq 0\}, \] where \(\{y\}\) denotes the fractional part of the real number \(y\).Inspired by previous works of J. Nilsson [Isr. J. Math. 171, 93–110 (2009; Zbl 1189.11038)] and Y. B. Pesin [Dimension theory in dynamical systems: contemporary views and applications. Chicago: Univ. Chicago Press (1997; Zbl 0895.58033)], the author determines the Hausdorff dimension of \(F_c^q\). From the abstract: This dimension “can be calculated using the spectral radius of the transition matrix of the corresponding subshift”. Reviewer: Georges Grekos (St. Étienne) Cited in 2 Documents MSC: 11K38 Irregularities of distribution, discrepancy 11K06 General theory of distribution modulo \(1\) Keywords:base-\(q\) expansion; Hausdorff dimension; non-dense orbit Citations:Zbl 0895.58033; Zbl 1189.11038 PDFBibTeX XMLCite \textit{F. Pausinger} and \textit{W. Ch. Schmid}, Unif. Distrib. Theory 6, No. 2, 31--46 (2011; Zbl 1313.11096)