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Cantor singular continuous spectrum for operators along interval exchange transformations. (English) Zbl 1134.47020

In the main theorem of this article, it is shown that for Schrödinger operators with potentials along the shift embedding of Lebesgue almost every interval exchange transformations, the spectrum is a Cantor set of measure zero and pure singular continuous for Lebesgue almost all points of the interval.

MSC:

47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37B10 Symbolic dynamics
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