2012/08/31 by Rafael Tiedra de Aldecoa, R. TIEDRA DE ALDECOA
Mathematics · Physics and Astronomy · #Absolute continuity #Advanced Operator Algebra Research #Commutator #Dynamical systems theory #Ergodic theory #Ergodicity #Mathematical Dynamics and Fractals #Skew #Spectral Theory in Mathematical Physics #Spectral analysis #Spectrum (functional analysis) #math-ph #math.DS #math.MP #math.SP #msc:37A30 #msc:37C10 #msc:37C40 #msc:37D40 #msc:58J51 #msc:81Q10
paper · pdf · doi:10.1017/etds.2013.76
published as Ergod. Th. Dynam. Sys. 35 (2015) 944-967 · corrections and simplifications in section 4
arxiv created 2012/09/11 · openalex publication_date 2014/01/10 · openalex created_date 2016/06/24 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05
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 those to be found in the literature, and for skew products over translations and Furstenberg transformations we obtain countable Lebesgue spectrum under assumptions not previously covered in the literature.