For a nonautonomous differential equation, we consider the almost reducibility property that corresponds to the reduction of the original equation to anautonomous equation via a coordinate change preserving the Lyapunov exponents. Inparticular, we characterize the class of equations to which a given equation is almostreducible. The proof is based on a characterization of the almost reducibility to an autonomous equation with a diagonal coefficient matrix. We also characterize the notionof almost reducibility for an equation x0 = A(t, θ)x depending continuously on a realparameter θ. In particular, we show that the almost reducibility set is always an Fσδ-setand for any Fσδ-set containing zero we construct a differential equation with that set asits almost reducibility set.
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