Compound matrices and ordinary differential equations

Abstract

A survey is given of a connection between compound matrices and ordinary differential equations. Some typical linear results are presented. For nonlinear autonomous systems, a criterion for orbital asymptotic stability of a closed trajectory given by Poincaré in two dimensions is extended to systems of any finite dimension. A criterion of Bendixson for the nonexistence of periodic solutions of a two dimensional system is also extended to higher dimensional systems. © 1990 Rocky Mountain Journal of Mathematics.