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arXiv · 0809.0150

Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions

Aris Daniilidis·Olivier Ley·Stéphane Sabourau
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Abstract

We hereby introduce and study the notion of self-contracted curves, which encompasses orbits of gradient systems of convex and quasiconvex functions. Our main result shows that bounded self-contracted planar curves have a finite length. We also give an example of a convex function defined in the plane whose gradient orbits spiral infinitely many times around the unique minimum of the function.

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Aris Daniilidis, Olivier Ley, Stéphane Sabourau. 2008-08-31. Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions. https://doi.org/10.1016/j.matpur.2010.03.007

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