Gradient flow of a harmonic function in

Abstract: In the paper I study the gradient field of a harmonic function f in in a neighborhood of a critical point 0. I show that the flow of ∇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 ∇f posed by R. Thom. I also show that the trajectories of ∇f having 0 as a limit point satisfy the finiteness conjecture and have generalized tangents at 0. [Copyright &y& Elsevier]