{"paper":{"title":"Disjointness of rescalings of smooth area preserving flows on surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Corinna Ulcigrai, Przemys{\\l}aw Berk","submitted_at":"2026-06-09T11:21:52Z","abstract_excerpt":"We consider the problem of \\emph{disjointness of rescalings} $(\\varphi_{\\kappa t})_{t\\in \\mathbb{R}}$, $\\kappa\\in\\mathbb{R}$ of a flow $(\\varphi_{t})_{t\\in \\mathbb{R}}$ in the context of smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces. We show that, when the genus of the surface is $g\\ge 2$, almost every locally Hamiltonian flow with 2g-2 non-degenerate simple saddles is such that any distinct two rational rescalings $(\\varphi_{\\kappa t})_{t\\in \\mathbb{R}}$ and $(\\varphi_{\\kappa' t})_{t\\in \\mathbb{R}}$ with $\\kappa="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10714","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10714/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}