{"paper":{"title":"Vector Fields with the Oriented Shadowing Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergei Yu. Pilyugin, Sergey Tikhomirov","submitted_at":"2010-10-16T02:29:05Z","abstract_excerpt":"We give a description of the $\\Cone$-interior ($\\Int^1(\\OrientSh)$) of the set of smooth vector fields on a smooth closed manifold that have the oriented shadowing property. A special class $\\Bb$ of vector fields that are not structurally stable is introduced. It is shown that the set $\\Int^1(\\OrientSh\\setminus\\Bb)$ coincides with the set of structurally stable vector fields. An example of a field of the class $\\Bb$ belonging to $\\Int^1(\\OrientSh)$ is given. Bibliography: 18 titles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3308","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"}