{"paper":{"title":"On the continuity of F{\\o}lner averages","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Fuhrmann, Maik Gr\\\"oger, Till Hauser","submitted_at":"2023-03-30T07:00:23Z","abstract_excerpt":"It is known that if each point $x$ of a dynamical system is generic for some invariant measure $\\mu_x$, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group is abelian and the map $x\\mapsto \\mu_x$ is continuous, then every orbit closure is uniquely ergodic.\n  In this note, we show that if the acting group is not abelian, orbit closures may well support more than one ergodic measure even if $x\\mapsto \\mu_x$ is continuous. We provide examples of such a situation via actions of the group of all orientation-preservi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.17191","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/2303.17191/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"}