Criterion for Lyapunov Reducibility of a Linear Autonomous Differential System to a Linear Autonomous Equation.

We establish a unified criterion for the reducibility of a linear homogeneous differential system with constant coefficients to a linear homogeneous differential equation with constant coefficients by means of both Lyapunov and periodic transformations. The resulting necessary and sufficient condition on a system is formulated in terms of properties of the Jordan normal form of its matrix. [ABSTRACT FROM AUTHOR]