{"paper":{"title":"Ergodic properties of invariant measures for systems with average shadowing property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Xiaoping Yuan, Xueting Tian, Yiwei Dong","submitted_at":"2013-12-02T00:26:04Z","abstract_excerpt":"In this paper, we explore a topological system $f:M\\rightarrow M$ with average shadowing property. We extend Sigmund's results and show that every non-empty, compact and connected subset $V\\subseteq\\mathcal {M}_{inv}(f)$ coincides with $V_f(y)$, where $\\mathcal {M}_{inv}(f)$ denotes the space of invariant Borel probability measures on M, and $V_f(y)$ denotes the accumulation set of time average of Dirac measures supported at the orbit of $y$. We also show that the set $M_{V}=\\{y\\in M\\,\\,|\\,\\,V_{f}(y)=V\\}$ is dense in $\\Delta_{V}=\\bigcup_{\\nu\\in V}supp(\\nu)$. In particular, if $\\Delta_{max}=\\bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0292","kind":"arxiv","version":3},"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"}