English

Commutator methods for the spectral analysis of uniquely ergodic dynamical systems

Dynamical Systems 2019-02-20 v2 Mathematical Physics math.MP Spectral Theory

Abstract

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 translations and Furstenberg transformations. For time changes of horocycle flows, we obtain absolute continuity under assumptions weaker than the ones to be found in the literature.

Keywords

Cite

@article{arxiv.1208.3784,
  title  = {Commutator methods for the spectral analysis of uniquely ergodic dynamical systems},
  author = {Rafael Tiedra de Aldecoa},
  journal= {arXiv preprint arXiv:1208.3784},
  year   = {2019}
}

Comments

corrections and simplifications in section 4

R2 v1 2026-06-21T21:52:32.805Z