Absolutely continuous cocycles over irrational rotations

DOI10.1007/BF02764637zbMath0786.28011OpenAlexW2104785628MaRDI QIDQ690044

Daniel J. Rudolph, Anzelm Iwanik, Mariusz Lemanczyk

Publication date: 26 April 1994

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02764637

zbMATH Keywords

irrational rotationergodic transformationsAnzai skew productscountable Lebesgue spectrummaximal spectral type

Mathematics Subject Classification ID

Measure-preserving transformations (28D05)

Related Items (19)

On the degree of cocycles with values in the group SU(2) ⋮ Informal research statement ⋮ Rigidity and non-recurrence along sequences ⋮ Commutator methods for unitary operators ⋮ Absolutely continuous spectrum for parabolic flows/maps ⋮ The absolute continuous spectrum of skew products of compact Lie groups ⋮ A class of compact group extensions of \(\beta \)-transformations ⋮ Nilpotent extensions of Furstenberg transformations ⋮ On functions that are trivial cocycles for a set of irrationals. II ⋮ Tracial Rokhlin property for automorphisms on simple -algebras ⋮ Commutator criteria for strong mixing ⋮ Ergodic properties of real cocycles and pseudo-homogeneous Banach spaces ⋮ Skew products over translations on ${\mathbf T}^d$, $d \geq 2$ ⋮ Spectral Types of Uniform Distribution ⋮ Approximate transitivity property and Lebesgue spectrum ⋮ Furstenberg transformations on Cartesian products of infinite-dimensional tori ⋮ Upper bounds for the spectral multiplicity of operators associated with regular cocycles ⋮ Ratner’s property for special flows over irrational rotations under functions of bounded variation ⋮ Commutator methods for the spectral analysis of uniquely ergodic dynamical systems

Cites Work

• Skew products over the irrational rotation
• Ergodic measure preserving transformations with arbitrary finite spectral multiplicities
• Toeplitz \(Z_ 2\)-extensions
• Transformations with highly nonhomogeneous spectrum of finite multiplicity
• A Measure Preserving Transformation whose Spectrum has Lebesgue Component of Multiplicity Two
• Ensemble d'invariants pour les produits croisés de Anzai
• On the multiplicity function of ergodic group extensions of rotations
• Strict Ergodicity and Transformation of the Torus
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