{"paper":{"title":"Variational equalities of entropy in nonuniformly hyperbolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chao Liang, Gang Liao, Wenxiang Sun, Xueting Tian","submitted_at":"2011-10-27T14:31:02Z","abstract_excerpt":"In this paper we prove that for an ergodic hyperbolic measure $\\omega$ of a $C^{1+\\alpha}$ diffeomorphism $f$ on a Riemannian manifold $M$, there is an $\\omega$-full measured set $\\widetilde{\\Lambda}$ such that for every invariant probability $\\mu\\in \\mathcal{M}_{inv}(\\widetilde{\\Lambda},f)$, the metric entropy of $\\mu$ is equal to the topological entropy of saturated set $G_{\\mu}$ consisting of generic points of $\\mu$: $$h_\\mu(f)=h_{\\top}(f,G_{\\mu}).$$ Moreover, for every nonempty, compact and connected subset $K$ of $\\mathcal{M}_{inv}(\\widetilde{\\Lambda},f)$ with the same hyperbolic rate, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6091","kind":"arxiv","version":2},"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"}