2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222442Exploiting 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.20 pagesDynamical Systems37A15, 37A25, 37A30.text