{"paper":{"title":"On the complexity of upper frequently hypercyclic vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DS","math.GN"],"primary_cat":"math.FA","authors_text":"Paolo Leonetti, Szymon Glab","submitted_at":"2025-06-27T15:51:22Z","abstract_excerpt":"Given a continuous linear operator $T:X\\to X$, where $X$ is a topological vector space, let $\\mathrm{UFHC}(T)$ be the set of upper frequently hypercyclic vectors, that is, the set of vectors $x \\in X$ such that $\\{n \\in \\omega: T^nx \\in U\\}$ has positive upper asymptotic density for all nonempty open sets $U\\subseteq X$. It is known that $\\mathrm{UFHC}(T)$ is a $G_{\\delta\\sigma\\delta}$-set which is either empty or contains a dense $G_{\\delta}$-set. Using a purely topological proof, we improve it by showing that $\\mathrm{UFHC}(T)$ is always a $G_{\\delta\\sigma}$-set.\n  Bonilla and Grosse-Erdmann"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22341","kind":"arxiv","version":1},"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/2506.22341/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"}