Proof of the gradient conjecture of R. Thom

@article{Kurdyka1999ProofOT,
  title={Proof of the gradient conjecture of R. Thom},
  author={Krzysztof Kurdyka and Tadeusz Mostowski and Adam Parusinski},
  journal={Annals of Mathematics},
  year={1999},
  volume={152},
  pages={763-792}
}
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 )a tx0 have a limit. Actually we show a stronger statement: the radial projection of x(t) from x0 onto the unit sphere has flnite length. 
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