SPECTRUM OF MULTIDIMENSIONAL DYNAMICAL-SYSTEMS WITH POSITIVE ENTROPY

Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinai 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(infinity)-actions. Next, using its relative version, we extend to Z(infinity)-actions some other general results connecting spectrum and entropy.