On trajectories of analytic gradient vector fields

Abstract

Let f: Rn, 0 → R, 0 be an analytic function defined in a neighbourhood of the origin, having a critical point at 0. We show that the set of non-trivial trajectories of the equation x = ∇ f (x) attracted by the origin has the same Čech-Alexander cohomology groups as the real Milnor fibre of f. © 2002 Elsevier Science (USA).