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

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Reducibility or nonuniform hyperbolicity for quasiperiodic Schrodinger cocycles (2003, background): “This point of view, which has already been used in the study of reducibility properties of quasiperiodic cocycles with values in SU(2) and SL(2, R), has proved to be very useful in the nonperturbative case (see [ K1 ], [K2]).”
Numerical computation of the normal behaviour of invariant curves of n-dimensional maps (2001, background): “In some contexts [26–28], it is common to require the matrices A(θ) to belong to some special subgroup of matrices.”
Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications (2012, background): “reducibility of quasi-periodic cocycles (reducibility of a cocycle which is not necessarily close to a constant) is being developed rapidly. Based on Kotani theory [24, 33] and renormalization scheme [25], Avila and Krikorian [8] proved that: if αis recurrent Diophantine, A ∈ Cω 0(T,SL(2,R)), then f”