Abstract
In the paper [Differ. Uravn., 2007, vol. 43, no. 2, pp. 191–202], we defined the noncoinciding irreducibility sets N 2(a, σ) and N 3(a, σ), σ ∈ (0, 2a], of all n-dimensional linear differential systems with piecewise continuous coefficient matrices A(t) bounded on the half-line [0,+∞) with norms ||A(t)|| ≤ a < +∞ for each of which there exists a linear differential system that cannot be reduced to it by Lyapunov transformations and whose coefficient matrix B(t) satisfies the condition ||B(t) - A(t)|| ≤ const × e −σt, t ≥ 0, or the more general condition that the Lyapunov exponent of the difference B(t) - A(t) does not exceed -σ, respectively. In the present paper, we study the properties of irreducibility sets treated as functions of the parameters σ and a.
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Izobov, N.A. and Mazanik, S.A., A General Test for the Reducibility of Linear Differential Systems, and the Properties of the Reducibility Coefficient, Differ. Uravn., 2007, vol. 43, no. 2, pp. 191–202.
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Original Russian Text © N.A. Izobov, S.A. Mazanik, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 8, pp. 979–989.
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Izobov, N.A., Mazanik, S.A. Parametric properties of irreducibility sets of linear differential systems. Diff Equat 51, 973–983 (2015). https://doi.org/10.1134/S0012266115080017
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DOI: https://doi.org/10.1134/S0012266115080017