{"paper":{"title":"On the F-expanding of Homoclinic class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bo Li, Wanlou Wu","submitted_at":"2017-10-23T20:06:47Z","abstract_excerpt":"We establish a closing property for thin trapped homoclinic classes. Taking advantage of this property, we proved that if the homoclinic class $H(p)$ admits a dominated splitting $T_{H(p)}M=E\\oplus_{<}F$, where $E$ is thin trapped (see Definition \\ref{Def:TP}) and all periodic points homoclinically related to $p$ are uniformly $F$-expanding at the period (see Definition \\ref{Def:expanding}), then $F$ is expanded (see Definition \\ref{Def:TP})."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08487","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"}