Gradient flow of a harmonic function in R3

In the paper I study the gradient field of a harmonic function f in R-3 in a neighborhood of a critical point 0. I show that the flow of del f, as a mapping between level sets of f, is a stratified mapping - that gives, in our case, an answer to the problem of stratifying the space of orbits of the field del f posed by R. Thom. I also show that the trajectories of del f having 0 as a limit point satisfy the finiteness conjecture and have generalized tangents at 0. (C) 2009 Elsevier Inc. All rights reserved.