On the spectrum of $α$-rigid maps

Details On the spectrum of $α$-rigid maps On the spectrum of $α$-rigid maps

2009-02-16

arxiv.org/abs/0902.2622v4

Journal of Dynamical and Control Systems Vol. 15, No. 4, (2009) 453?470

Mathematics

Dynamical Systems

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

Scientific paper

10.1007/s10883-009-9076-x

It is shown that there exists an $\alpha$-rigid transformation with $\alpha$
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 $\alpha$-rigid transformations with singular
spectrum.

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