{"paper":{"title":"Observable Optimal State Points of Sub-additive Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eleonora Catsigeras, Yun Zhao","submitted_at":"2011-09-30T03:53:58Z","abstract_excerpt":"For a sequence of sub-additive potentials, Dai [Optimal state points of the sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method of choosing state points with negative growth rates for an ergodic dynamical system. This paper generalizes Dai's result to the non-ergodic case, and proves that under some mild additional hypothesis, one can choose points with negative growth rates from a positive Lebesgue measure set, even if the system does not preserve any measure that is absolutely continuous with respect to Lebesgue measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6710","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"}