{"paper":{"title":"Polycycle omega-limit sets of flows on the compact Riemann surfaces and Eulerian path","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hahng-Yun Chu, Jaeyoo Choy","submitted_at":"2016-09-27T15:49:35Z","abstract_excerpt":"Let $(S,\\Phi)$ be a pair of a closed oriented surface and $\\Phi$ be a real analytic flow with finitely many singularities. Let $x$ be a point of $S$ with the polycycle $\\omega$-limit set $\\omega(x)$. In this paper we give topological classification of $\\omega(x)$. Our main theorem says that $\\omega(x)$ is diffeomorphic to the boundary of a cactus in the $2$-sphere $S^{2}$. Moreover $S$ is a connected sum of the above $S^{2}$ and a closed oriented surface along finitely many embedded circles which are disjoint from $\\omega(x)$. This gives a natural generalization to the higher genus of the main"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08505","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"}