×

Non-integer bases, iteration of continuous real maps, and an arithmetic self-similar set. (English) Zbl 1012.11007

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.

MSC:

11A63 Radix representation; digital problems
37E99 Low-dimensional dynamical systems
PDFBibTeX XMLCite
Full Text: DOI