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

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

2008-08-31

arxiv.org/abs/0809.0150v1

Journal de Math\'ematiques Pures et Appliqu\'es 94 (2010) 183-199

Mathematics

Dynamical Systems

Scientific paper

10.1016/j.matpur.2010.03.007

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.

Affiliated with

Also associated with

No associations

Rating

Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-363955