{"paper":{"title":"A spectral-like decomposition for transitive Anosov flows in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bin Yu, Christian Bonatti, Fran\\c{c}ois B\\'eguin","submitted_at":"2015-05-23T01:52:11Z","abstract_excerpt":"Given a (transitive or non-transitive) Anosov vector field $X$ on a closed three-dimensional manifold $M$, one may try to decompose $(M,X)$ by cutting $M$ along two-tori transverse to $X$. We prove that one can find a finite collection $\\{T_1,\\dots,T_n\\}$ of pairwise disjoint, pairwise non-parallel incompressible tori transverse to $X$, such that the maximal invariant sets $\\Lambda_1,\\dots,\\Lambda_m$ of the connected components $V_1,\\dots,V_m$ of $M-(T_1\\cup\\dots\\cup T_n)$ satisfy the following properties: 1, each $\\Lambda_i$ is a compact invariant locally maximal transitive set for $X$, 2, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06259","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"}