{"paper":{"title":"Common hypercyclic vectors for high dimensional families of operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Fr\\'ed\\'eric Bayart","submitted_at":"2015-03-30T07:45:57Z","abstract_excerpt":"Let $(T\\_\\lambda)\\_{\\lambda\\in\\Lambda}$ be a family of operators acting on a $F$-space $X$, where the parameter space $\\Lambda$ is a subset of $\\mathbb R^d$. We give sufficient conditions\non the family to yield the existence of a vector $x\\in X$ such that, for any $\\lambda\\in\\Lambda$, the set $\\big\\{T\\_\\lambda^n x;\\ n\\geq 1\\big\\}$ is dense in $X$. We obtain results valid for any value of $d\\geq 1$ whereas the previously known results where restricted to $d=1$. Our methods also shed new light on the one-dimensional case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08574","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":""},"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"}