{"paper":{"title":"Dynamics of riemannian 1-foliations on $3$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DS","authors_text":"Hahng-Yun Chu, Jaeyoo Choy","submitted_at":"2009-03-26T11:12:58Z","abstract_excerpt":"In this paper we study several dynamical properties of the riemannian $1$-dimensional foliation $\\mathcal{L}$ on an oriented closed 3-manifold $M$. Carriere classified such pairs $(M,\\mathcal{L})$. Using the classification we prove the nonhyperbolicity of $(M,\\mathcal{L})$. Also we describe in detail recurrence points, $\\omega$-limit sets and attractors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4546","kind":"arxiv","version":4},"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"}