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.
A sufficient condition for dichotomy based on a suitable invariance property / L. Consolini; M. Tosques. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 251:6(2011), pp. 1475-1488. [10.1016/j.jde.2011.05.028]
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