{"paper":{"title":"Gradient flows, second order gradient systems and convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aris Daniilidis, Philippe Cieutat, Tahar Boulmezaoud","submitted_at":"2017-10-21T22:19:47Z","abstract_excerpt":"We disclose an interesting connection between the gradient flow of a $\\mathcal{C}^2$-smooth function $\\psi$ and evanescent orbits of the second order gradient system defined by the square-norm of $\\nabla\\psi$, under adequate convexity assumption. As a consequence, we obtain the following surprising result for two $\\mathcal{C}^2$, convex and bounded from below functions $\\psi_1$, $\\psi_2$: if $||\\nabla\\psi_1||=||\\nabla\\psi_2||$, then $\\psi_1=\\psi_2 + k$, for some $k\\in \\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07858","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}