{"paper":{"title":"Subcohomology and a Livsic Theorem for Zooming Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eduardo Santana, Lamine Mbarki","submitted_at":"2022-08-28T12:27:11Z","abstract_excerpt":"In the context of continuous zooming systems $f:M \\to M$ on a compact metric space $M$, which include the non-uniformly expanding ones, possibly with the presence of a critical set, with the zooming set dense in $M$, we prove that any H\\\"older potential $\\phi : M \\to \\mathbb{R}$ for which the integrals $\\int \\phi d\\mu \\geq 0$ with respect to any $f$-invariant probability $\\mu$, admits a continuous function $\\lambda_{0} : M \\to \\mathbb{R}$ (which can be H\\\"older if some integral is positive) such that\n  \\[\n  \\phi \\geq \\lambda_{0}- \\lambda_{0} \\circ f.\n  \\]\n  This extends a result in [9] for $C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.13209","kind":"arxiv","version":6},"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/2208.13209/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"}