Gradient vector fields do not generate twister dynamics (Q5944083)

The goal of this paper is to prove property that there is no ``spiraling axis'' \(\Gamma\) for \(\gamma\), where \(\gamma\) is a solution for analytic gradient vector fields when \(\Gamma\) is not a union of stationary points. These axes are called ``twister axis'' and they give rise to a twister dynamics locally around them. The authors prove, in dimension 3, that if \(\gamma\) is ``infinitely near'' an analytic curve \(\Gamma\) not composed of singularities of \(X\), then \(\gamma\) is non-oscillating, furthermore it does not spiral around \(\Gamma\) in a precise sense.