{"paper":{"title":"On the Transitivity of Invariant Manifolds of Conservative Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F\\'abio Castro, Fernando Oliveira","submitted_at":"2015-02-28T21:23:35Z","abstract_excerpt":"The main result of this work is the following: for volume preserving flows on compact manifolds with the $C^r$ topology, $1 \\leqq r \\leqq \\infty$ , the closure of every invariant manifold of periodic orbits and singularities is a chain transitive set.\n  We also develop to new local constructions, which surprise by the simplicity of the arguments. One, a local perturbation to change an orbit to a nearby without altering its past. The other is a flow box theorem in the context of volume preserving flows, a result that is well known for Hamiltonians or general flows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00182","kind":"arxiv","version":3},"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"}