Half a Century with the Problem of the Gradient of an Analytic Function
摘要
This is a review concerning the study of the local dynamics of a gradient vector field of a real analytic function. Starting from the famous Thom’s Gradient Conjecture, we discuss the state of art of the Finiteness Conjecture on non-oscillation of trajectories and we end with the formulation of the problem in the context of o-minimal geometry.