{"paper":{"title":"A note on shadowing properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dae Hwan Goo, Hahng-Yun Chu, Se-Hyun Ku","submitted_at":"2016-09-29T17:50:54Z","abstract_excerpt":"Let $\\mathfrak{X}^{1}(M)$ be the space of $C^{1}$-vector fields on $M$ endowed with the $C^{1}$-topology and let $\\Lambda$ be an isolated set for a $X\\in\\mathfrak{X}^{1}(M)$. In this paper, we directly prove that every $X\\in\\mathfrak{X}^{1}(M)$ having the (asymptotic) average shadowing property in $\\Lambda$ has no proper attractor in $\\Lambda$. Our proof is a direct version of the results by Gu and Ribeiro. We also show that every $X\\in\\mathfrak{X}^{1}(M)$ having the (two-sided) limit shadowing property with a gap in $\\Lambda$ is topologically transitive and has the shadowing property in $\\Lam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09439","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"}