Linearly recurrent circle map subshifts and an application to Schrödinger operators (Q1854635)

The authors consider the discrete, one-dimensional Schrödinger operators with potentials generated by circle maps [\textit{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 [\textit{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.