Allouche, J.-P.; Cosnard, M. Non-integer bases, iteration of continuous real maps, and an arithmetic self-similar set. (English) Zbl 1012.11007 Acta Math. Hung. 91, No. 4, 325-332 (2001). Summary: We prove that a recent result of V. Komornik and P. Loreti [Rend. Mat. Appl. (7) 19, 615-634 (1999; Zbl 0963.11006)] on the smallest real number \(q\) in \((1,2)\) such that the number 1 admits a unique \(q\)-expansion can be deduced from a result of the authors [Publ. Math. Orsay 83-04, 1-7 (1983; Zbl 0562.54066)] on kneading sequences occurring when iterating continuous maps of the interval. We also give arithmetic results related to this problem. Cited in 14 Documents MSC: 11A63 Radix representation; digital problems 37E99 Low-dimensional dynamical systems Keywords:non-integer bases; unique \(q\)-expansion Citations:Zbl 0963.11006; Zbl 0562.54066 PDFBibTeX XMLCite \textit{J. P. Allouche} and \textit{M. Cosnard}, Acta Math. Hung. 91, No. 4, 325--332 (2001; Zbl 1012.11007) Full Text: DOI