{"paper":{"title":"The Structure on Invariant Measures of $C^1$ generic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Wenxiang Sun, Xueting Tian","submitted_at":"2010-04-20T13:15:27Z","abstract_excerpt":"Let $\\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism $f\\in\\Diff(M)$. We show that the space of invariant measures supported on $\\Lambda$ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in $\\Lambda$ (which implies the set of irregular$^+$ points is also residual in $\\Lambda$). As an application, we show that the non-uniform hyperbolicity of irregular$^+$ points in $\\Lambda$ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in $\\Lambda$)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3439","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"}