Adamczewski, B.; Damanik, D. Linearly recurrent circle map subshifts and an application to Schrödinger operators. (English) Zbl 1023.47019 Ann. Henri Poincaré 3, No. 5, 1019-1047 (2002). The authors consider the discrete, one-dimensional Schrödinger operators with potentials generated by circle maps [D. Lenz, Commun. Math. Phys. 227, 119-130 (2002; Zbl 1065.47035)], where each potential contains two parameters. The set of these parameters are characterized so that the corresponding circle map is linearly recurrent [F. Durand, Ergodic Theory Dyn. Syst. 20, 1061-1078 (2000; Zbl 0965.37013)]. This property allows the authors to conclude that the discrete Schrödinger operator has a purely singular continuous spectrum supported on a Cantor set of zero Lebesgue measure. Reviewer: Hyeona Lim (Mississippi) Cited in 7 Documents MSC: 47B39 Linear difference operators 39A70 Difference operators 37E10 Dynamical systems involving maps of the circle 37B20 Notions of recurrence and recurrent behavior in topological dynamical systems Keywords:linear recurrence; Schrödinger operator; circle map; spectral theory; purely singular continuous spectrum; Cantor set of zero Lebesgue measure Citations:Zbl 1065.47035; Zbl 0965.37013 PDFBibTeX XMLCite \textit{B. Adamczewski} and \textit{D. Damanik}, Ann. Henri Poincaré 3, No. 5, 1019--1047 (2002; Zbl 1023.47019) Full Text: DOI