On the spectrum of $\alpha$-rigid maps

Abstract

It is shown that there exists an $\alpha$-rigid transformation with $\alpha$ less or equal to $\frac{1}{2}$ 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 $\alpha$-rigid transformations with singular spectrum.

15 pages. Accepted for publication in Journal of Dynamical and Control Systems

References in corpus (1)

• Weak mixing of maps with bounded cutting parameter

Cited by in corpus (1)

• Rigidity Sequences of Power Rationally Weakly Mixing Transformations