{"paper":{"title":"Hypercyclic tuples of operators on $C^n$ and $R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Stanislav Shkarin","submitted_at":"2010-08-20T12:21:43Z","abstract_excerpt":"A tuple $(T_1,\\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In particular, we prove that the minimal cardinality of a hypercyclcic tuple of operators on $C^n$ (respectively, on $R^n$) is $n+1$ (respectively, $\\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3483","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"}