A sufficient condition for dichotomy based on a suitable invariance property

In this paper we introduce a cone invariance property, which ensures dichotomy for a linear differential system under suitable technical conditions.This property consists in the existence of two disjoint cones, such that the forward (backward) flow originating from a plane that lies in the first (second) cone remains in the cone itself. This property can be verified even if the system matrix is not diagonal dominant. As a consequence, the resulting conditions for dichotomy are not related to diagonal dominance and can be applied to cases in which some of the classical hypotheses appearing in literature do not hold.