{"paper":{"title":"Structure of the endpoint map near nice singular curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DG","authors_text":"Andrei A. Agrachev, Francesco Boarotto","submitted_at":"2018-10-30T11:19:41Z","abstract_excerpt":"Given a rank-two sub-Riemannian structure $(M,\\Delta)$ and a point $x_0\\in M$, a singular curve is a critical point of the endpoint map $F:\\gamma\\mapsto\\gamma(1)$ defined on the space of horizontal curves starting at $x_0$. The typical least degenerate singular curves of these structures are called \\emph{regular singular curves}; they are \\emph{nice} if their endpoint is not conjugate along $\\gamma$. The main goal of this paper is to show that locally around a nice singular curve $\\gamma$, once we choose a suitable topology on the control space we can find a normal form for the endpoint map, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12662","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"}