26 citations · 63 across the 25 of their papers we have counts for
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A convex function satisfying the Lojasiewicz inequality but failing the gradient conjecture both at zero and infinity
Aris Daniilidis, Mounir Haddou, Olivier Ley
We construct an example of a smooth convex function on the plane with a strict minimum at zero, which is real analytic except at zero, for which Thom's gradient conjecture fails bo…
Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions
Aris Daniilidis, Olivier Ley, Stéphane Sabourau
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 bou…
On the first integral conjecture of Rene Thom
Jacky Cresson, Aris Daniilidis, Masahiro Shiota
More that half a century ago R. Thom asserted in an unpublished manuscript that, generically, vector fields on compact connected smooth manifolds without boundary can admit only tr…