Proof of the gradient conjecture of R. Thom. (Q5931223)

Let \(x(t)\) be a trajectory of the gradient of a real analytic function and suppose that \(x_0\) is a limit point of \(x(t)\). In this important paper the authors prove the gradient conjecture of R. Thom which states that the secants of \(x(t)\) at \(x_0\) have a limit. Actually they show a stronger statement: the radial projection of \(x(t)\) from \(x_0\) onto the unit sphere has finite length.