# On the spectrum of $α$-rigid maps - Mathematics > Dynamical Systems

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Abstract: It is shown that there exists an $\alpha$-rigid transformation with $\alpha$less or equal to $\frac12$ whose spectrum has Lebesgue component. This answersthe question raised by Klemes and Reinhold in \cite{Klemes-Reinhold}. Weexhibit also a large class of $\alpha$-rigid transformations with singularspectrum.

Author: El Houcein El Abdalaoui LMRS

Source: https://arxiv.org/