Stability of gradient systems (Q5903725)

Consider two gradient systems in \({\mathbb{R}}^ n.\) Let \(x_ 0\) be an asymptotically stable equilibrium for both systems. Suppose both potentials are C 1, and \(n\neq 3,4,5\). It is proved that under these conditions the systems can be ``connected by nondegenerate deformations'', which means a homotopy along gradient systems with isolated equilibrium \(x_ 0\).