{"paper":{"title":"On the density of singular hyperbolic three-dimensional vector fields: a conjecture of Palis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawei Yang, Sylvain Crovisier","submitted_at":"2014-04-21T07:37:29Z","abstract_excerpt":"In this note we announce a result for vector fields on three-dimensional manifolds: those who are singular hyperbolic or exhibit a homoclinic tangency form a dense subset of the space of $C^1$-vector fields. This answers a conjecture by Palis. The argument uses an extension for local fibered flows of Ma\\~n\\'e and Pujals-Sambarino's theorems about the uniform contraction of one-dimensional dominated bundles.\n  Sur la densit\\'e de l'hyperbolicit\\'e singuli\\`ere pour les champs de vecteurs en dimension trois : une conjecture de Palis\n  Dans cette note, nous annon\\c{c}ons un r\\'esultat portant sur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5130","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"}