On strictly positively invariant cones (Q792417)

The main result is the following: Let A be a real \(n\times n\) matrix and C a proper closed convex cone in \({\mathbb{R}}^ n\) such that \(e^{tA}(C\backslash \{0\})\subseteq int(C)\) for all positive t. Then the boundary of the set of points with the property that the image under the action of \(e^{tA}\) is in C for some positive t is an (n-1)- dimensional A-invariant subspace. This is applied to stability of cones.