On a property of the reducibility exponent of linear differential systems
N. A. Izobov, С. А. Мазаник · Differential Equations · 2008
We establish that the reducibility exponent (Differentsial’nye Uravneniya, 2007, vol. 43, no. 2, pp. 191–202) of each linear system $$ \dot x = A(t)x, x \in \mathbb{R}^n , t \geqslant 0 $$ , with piecewise continuous bounded coefficient matrix A does not belong to the set of values of σ for which the perturbed system (1A+Q) with an arbitrary piecewise continuous perturbation Q satisfying the condition $$ \overline {\lim } _{t \to + \infty } t^{ - 1} \ln \left\| {Q(t)} \right\| \leqslant - \sigma $$ is reducible to the original system (1 A ) by some Lyapunov transformation.