Abstract
We present a relation between μ-dichotomy spectrum and Sacker-Sell spectrum. From this relation, we show that, under some suitable conditions, if the system x′=A(t)x admits a μ-dichotomy, then it admits an exponential dichotomy. Utilizing this result, we present a linearization theorem. Furthermore, we prove that the μ-dichotomy spectrum of the system x′=diag(A1(t),A2(t))x is the union of μ-dichotomy spectra of the subsystems x1′=A1(t)x1 and x2′=A2(t)x2, while this result is wrong if we replace μ-dichotomy spectrum with nonuniform exponential dichotomy spectrum. We also provide a new method to prove the μ-dichotomy spectral theorem.
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