Global density of reducible quasi-periodic cocycles on T1 x SU(2)

Raphäl Krikorian

doi:10.2307/3062098

Global density of reducible quasi-periodic cocycles on T¹ x SU(2)

Raphäl Krikorian

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that given α in a set of total (Haar) measure in T¹ = R/Z, the set of A ∈ C∞(T¹, SU(2)) for which the skew-product system (α, A) : T¹ x SU(2) → T¹ x SU(2), (α, A)(θ, y) = (θ + α, A(θ)y) is reducible - that is, A(·) = B(· + α)A₀B(·)^-1, for some A₀ ∈ SU(2), B ∈ C∞(T¹, SU(2)),-is dense for the C∞-topology.

Original language	English
Pages (from-to)	269-326
Number of pages	58
Journal	Annals of Mathematics
Volume	154
Issue number	2
DOIs	https://doi.org/10.2307/3062098
Publication status	Published - 1 Jan 2001

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title = "Global density of reducible quasi-periodic cocycles on T1 x SU(2)",

abstract = "We prove that given α in a set of total (Haar) measure in T1 = R/Z, the set of A ∈ C∞(T1, SU(2)) for which the skew-product system (α, A) : T1 x SU(2) → T1 x SU(2), (α, A)(θ, y) = (θ + α, A(θ)y) is reducible - that is, A(·) = B(· + α)A0B(·)-1, for some A0 ∈ SU(2), B ∈ C∞(T1, SU(2)),-is dense for the C∞-topology.",

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AB - We prove that given α in a set of total (Haar) measure in T1 = R/Z, the set of A ∈ C∞(T1, SU(2)) for which the skew-product system (α, A) : T1 x SU(2) → T1 x SU(2), (α, A)(θ, y) = (θ + α, A(θ)y) is reducible - that is, A(·) = B(· + α)A0B(·)-1, for some A0 ∈ SU(2), B ∈ C∞(T1, SU(2)),-is dense for the C∞-topology.

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Global density of reducible quasi-periodic cocycles on T1 x SU(2)

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Global density of reducible quasi-periodic cocycles on T¹ x SU(2)