On the singular and higher characteristic exponents of an almost periodic linear differential system with an affine dependence on a parameter

摘要

Consider the system x = A(t, μ)x, x ∈ Cn, t ≥ 0, with coefficient matrix A(t, μ) bounded and continuous with respect to t and analytic with respect to t, μ. It was shown in [1] that the higher exponent of this system, treated as a function of the parameter μ ∈ C, is upper semicontinuous for almost all μ ∈ C and has a continuous restriction to a set M whose complement in C has zero Lebesgue measure [2].