M. Cobo, C. Gutierrez, C. R. de Oliveira
Cantor Singular Continuous Spectrum for Operators Along Interval Exchange Transformations
(234K, pdf)

ABSTRACT.  It is shown that Schroedinger operators, with potentials along the shift embedding of 
Lebesgue almost every interval exchange transformations, have Cantor 
spectrum of measure zero and 
pure singular continuous for Lebesgue almost all points of the 
interval.