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- W2186073119 abstract "We continue our study of the local theory for quasiperiodic cocycles in $mathbb{T} ^{d} times G$, where $G=SU(2)$, over a rotation satisfying a Diophantine condition and satisfying a closeness-to-constants condition, by proving a dichotomy between measurable reducibility (and therefore pure point spectrum), and purely continuous spectrum in the space orthogonal to $L^{2}(mathbb{T} ^{d}) hookrightarrow L^{2}(mathbb{T} ^{d} times G)$. Subsequently, we describe the equivalence classes of cocycles under smooth conjugacy, as a function of the parameters defining their K.A.M. normal form. Finally, we derive a complete classification of the dynamics of one-frequency ($d=1$) cocycles over a Recurrent Diophantine rotation. All theorems will be stated sharply in terms of the number of frequencies $d$, but in the proofs we will always assume $d=1$, for simplicity in expression and notation." @default.
- W2186073119 created "2016-06-24" @default.
- W2186073119 creator A5003424957 @default.
- W2186073119 date "2017-11-20" @default.
- W2186073119 modified "2023-09-23" @default.
- W2186073119 title "Continuous Spectrum or Measurable Reducibility for Quasiperiodic Cocycles in $${mathbb{T} ^{d} times SU(2)}$$ T d × S U ( 2 )" @default.
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- W2186073119 doi "https://doi.org/10.1007/s00220-017-3034-3" @default.
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