Approximate transitivity property and Lebesgue spectrum

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dc.creatorAbdalaoui, El Houcein El
dc.creatorLemanczyk, Mariusz
dc.date2009-03-03
dc.date2009-03-08
dc.date.accessioned2026-07-07T12:49:33Z
dc.date.available2026-07-07T12:49:33Z
dc.descriptionExploiting a spectral criterion for a system not to be AT we give some new examples of zero entropy systems without the AT property. Our examples include those with finite spectral multiplicity -- in particular we show that the system arising from the Rudin-Shapiro substitution is not AT. We also show that some nil-rotations on a quotient of the Heisenberg group as well as some (generalized) Gaussian systems are not AT. All known examples of non AT-automorphisms contain a Lebesgue component in the spectrum.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0903.0503
dc.identifierhttp://arxiv.org/abs/0903.0503
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222442
dc.subjectDynamical Systems
dc.subject37A15, 37A25, 37A30.
dc.titleApproximate transitivity property and Lebesgue spectrum
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