Approximate transitivity property and Lebesgue spectrum
Dynamical Systems
2009-03-08 v2
Abstract
Exploiting 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.
Cite
@article{arxiv.0903.0503,
title = {Approximate transitivity property and Lebesgue spectrum},
author = {El Houcein El Abdalaoui and Mariusz Lemanczyk},
journal= {arXiv preprint arXiv:0903.0503},
year = {2009}
}
Comments
20 pages