{"paper":{"title":"Rigidity of a class of smooth singular flows on $\\mathbb T^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Kanigowski, Changguang Dong","submitted_at":"2018-11-01T01:58:50Z","abstract_excerpt":"We study joining rigidity in the class of von Neumann flows with one singularity. They are given by a smooth vector field $\\mathcal{X}$ on $\\mathbb T^2\\setminus \\{a\\}$, where $\\mathcal{X}$ is not defined at $a\\in \\mathbb T^2$. It follows that the phase space can be decomposed into a (topological disc) $D_\\mathcal{X}$ and an ergodic component $E_\\mathcal{X}=\\mathbb T^2\\setminus D_\\mathcal{X}$. Let $\\omega_\\mathcal{X}$ be the 1-form associated to $\\mathcal{X}$. We show that if $|\\int_{E_{\\mathcal{X}_1}}d\\omega_{\\mathcal{X}_1}|\\neq |\\int_{E_{\\mathcal{X}_2}}d\\omega_{\\mathcal{X}_2}|$, then the corr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00184","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"}