{"paper":{"title":"Ergodic optimization theory for a class of typical maps","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Leiye Xu, Wen Huang, Xiao Ma, Yiwei Zhang, Zeng Lian","submitted_at":"2019-04-03T11:07:29Z","abstract_excerpt":"In this article, we consider the weighted ergodic optimization problem of a class of dynamical systems $T:X\\to X$ where $X$ is a compact metric space and $T$ is Lipschitz continuous. We show that once $T:X\\to X$ satisfies both the {\\em Anosov shadowing property }({\\bf ASP}) and the {\\em Ma\\~n\\'e-Conze-Guivarc'h-Bousch property }({\\bf MCGBP}), the minimizing measures of generic H\\\"older observables are unique and supported on a periodic orbit. Moreover, if $T:X\\to X$ is a subsystem of a dynamical system $f:M\\to M$ (i.e. $X\\subset M$ and $f|_X=T$) where $M$ is a compact smooth manifold, the abov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01915","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.01915/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}