On trajectories of analytic gradient vector fields (Q701075)

The main result of the paper is the following Theorem: Let \(f: \mathbb{R}^n\), \(0\to \mathbb{R},\,0\) be a real analytic function defined in some neighbourhood of the origin. The set of non-trivial trajectories of the equation \(\dot x=\nabla f(x)\) attracted by the origin has the same Čech-Alexander cohomology groups as the real Milnor fibre of \(f\).