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H. Broer, C. Simó (1998)
Hill's equation with quasi-periodic forcing: resonance tongues, instability pockets and global phenomenaBoletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society, 29
ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 3, pp. 369–379. c Pleiades Publishing, Inc., 2006. Original Russian Text c A.V. Lipnitskii, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 3, pp. 347–355. ORDINARY DIFFERENTIAL EQUATIONS On the Singular and Higher Characteristic Exponents of an Almost Periodic Linear Differential System with an Affine Dependence on a Parameter A. V. Lipnitskii Institute of Mathematics, National Academy of Sciences, Minsk, Belarus Received December 15, 2004 DOI: 10.1134/S0012266106030074 Consider the system x ˙ = A(t, μ)x, x ∈ C , 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]. Rakhimberdiev proved an analog of the first of these results for the system x ˙ = A(t)x, x ∈ R,t ≥ 0, (1 ) with bounded piecewise continuous coefficient matrix A(t). More precisely, he showed [3] that the
Differential Equations – Springer Journals
Published: Apr 17, 2006
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