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Commutator methods for the spectral analysis of uniquely ergodic dynamical systems

Published online by Cambridge University Press:  10 January 2014

R. TIEDRA DE ALDECOA
R. TIEDRA DE ALDECOA*
Affiliation:
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile email rtiedra@mat.puc.cl
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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.

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Type
Research Article
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Ergodic Theory and Dynamical Systems , Volume 35 , Issue 3 , May 2015 , pp. 944 - 967
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© Cambridge University Press, 2014 

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