Gradient Flow of a Harmonic Function in R

In the paper I study the gradient eld of a harmonic function f in R3 in a neighbourhood of a critical point 0. I show that the ow of ∇f , as a mapping between level sets of f , is a strati ed mapping that gives, in our case, an answer to the problem of stratifying the space of orbits of the eld ∇f posed by R. Thom. I also show that the trajectories of ∇f having 0 as a limit point satisfy the niteness conjecture and have generalized tangents at 0.