Abstract
It is shown that for any α ∈ [0, 1/2], there exists an α-rigid transformation whose spectrum has a Lebesgue component. This answers the question posed by Klemes and Reinhold in [7]. We apply a certain correspondence between weak limits of powers of a transformation and their skew products.
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The author was supported in part by Max Planck Institute of Mathematics, Bonn and the Programme of Support of Leading Scientific Schools of the RF (project NSh-3038.2008.1).
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Ageev, O.N. Nonsingular α-rigid maps. J Dyn Control Syst 15, 449–452 (2009). https://doi.org/10.1007/s10883-009-9079-7
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DOI: https://doi.org/10.1007/s10883-009-9079-7