On the spectrum of $\alpha$-rigid maps

El Houcein El Abdalaoui (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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.

Mots clés: $\alpha$-rigid transformation; intervals exchange maps; Lebesgue spectrum; substitution; quasi-analyticity; joinings

Domaines: Systèmes dynamiques [math.DS]

El Houcein El Abdalaoui. On the spectrum of $\alpha$-rigid maps. Journal of Dynamical and Control Systems, 2009, Vol. 15 (No. 4,), pp.453-470. ⟨10.1007/s10883-009-9076-x⟩. ⟨hal-00361465v4⟩