1208.3784 (Rafael Tiedra de Aldecoa)

Commutator methods for the spectral analysis of uniquely ergodic
dynamical systems    [PDF]

Rafael Tiedra de Aldecoa

We present a method, based on commutator methods, for the spectral analysis of uniquely ergodic dynamical systems. When applicable, it leads to the absolute continuity of the spectrum of the corresponding unitary operators. As an illustration, we consider time changes of horocycle flows, skew products over translation flows and Furstenberg transformations. For time changes of horocycle flows (resp. skew products over translation flows) we obtain absolute continuity (resp. countable Lebesgue spectrum) under assumptions weaker than the ones to be found in the literature.

View original: http://arxiv.org/abs/1208.3784