# Proof of the gradient conjecture of R. Thom

### Abstract

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

DOI

https://doi.org/10.2307/2661354

## Authors

Krzysztof Kurdyka