Spectrum of multidimensional dynamical systems with positive entropy
Volume 108 / 1994
Studia Mathematica 108 (1994), 77-85
DOI: 10.4064/sm-108-1-77-85
Abstract
Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov $ℤ^d$-action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to $ℤ^∞$-actions. Next, using its relative version, we extend to $ℤ^∞$-actions some other general results connecting spectrum and entropy.
