Resumen de Proof of the gradient conjecture of R. Thom

Adam Parusinski, T. Mostowski, Krzysztof Kurdyka

• Let x(t) be a trajectory of the gradient of a real analytic function and suppose that x0 is a limit point of x(t). We prove the gradient conjecture of R. Thom which states that the secants of x(t) at x0 have a limit. Actually we show a stronger statement: the radial projection of x(t) from x0 onto the unit sphere has finite length.