{"paper":{"title":"Prescribed energy connecting orbits for gradient systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.DS","authors_text":"Andres Zuniga, Francesca Alessio, Piero Montecchiari","submitted_at":"2019-01-21T15:10:14Z","abstract_excerpt":"We are concerned with conservative systems $\\ddot{q}=\\nabla V(q), \\; q\\in\\mathbb{R}^N$ for a general class of potentials $V\\in C^1(\\mathbb{R}^N)$. Assuming that a given sublevel set $\\{V\\leq c\\}$ splits in the disjoint union of two closed subsets $\\mathcal{V}^c_-$ and $\\mathcal{V}^c_+$, for some $c\\in\\mathbb{R}$, we establish the existence of bounded solutions $q_c$ to the above system with energy equal to $-c$ whose trajectories connect $\\mathcal{V}^c_-$ and $\\mathcal{V}^c_+$. The solutions are obtained through an energy constrained variational method, whenever mild coerciveness properties ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06951","kind":"arxiv","version":1},"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"}