Commutator methods for the spectral analysis of uniquely ergodic dynamical systems

摘要

We present a method, based on commutator methods, for the spectral analysisof uniquely ergodic dynamical systems. When applicable, it leads to theabsolute continuity of the spectrum of the corresponding unitary operators. Asan illustration, we consider time changes of horocycle flows, skew productsover translations and Furstenberg transformations. For time changes ofhorocycle flows, we obtain absolute continuity under assumptions weaker thanthe ones to be found in the literature.