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arXiv · 1103.0729

On Hessian limit directions along non-oscillating gradient trajectories

Vincent Grandjean
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Abstract

Given a non-oscillating gradient trajectory G of a real analytic function f, we show that the limit v of the secants at the limit point O of G along the trajectory G is an eigen-vector of the limit of the direction of the Hessian matrix Hess (f) at O along G. The same holds true at infinity if the function is globally subanalytic. We also deduce some interesting estimates along the trajectory.

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Vincent Grandjean. 2011-03-03. On Hessian limit directions along non-oscillating gradient trajectories. https://doi.org/10.4153/cjm-2012-021-6

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