On the spectrum of $α$-rigid maps
arXiv:0902.2622 · doi:10.1007/s10883-009-9076-x
Abstract
It is shown that there exists an $α$-rigid transformation with $α$ less or equal to $\frac12$ whose spectrum has Lebesgue component. This answers the question raised by Klemes and Reinhold in \cite{Klemes-Reinhold}. We exhibit also a large class of $α$-rigid transformations with singular spectrum.
15 pages. Accepted for publication in Journal of Dynamical and Control Systems