{"paper":{"title":"$n$-supercyclic and strongly $n$-supercyclic operators in finite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Romuald Ernst","submitted_at":"2012-05-16T06:54:30Z","abstract_excerpt":"We prove that on $\\mathbb{R}^n$, there is no $N$-supercyclic operator with $1\\leq N< \\lfloor \\frac{n+1}{2}\\rfloor$ i.e. if $\\mathbb{R}^n$ has an $N$ dimensional subspace whose orbit under $T$ is dense in $\\mathbb{R}^n$, then $N$ is greater than $\\lfloor\\frac{n+1}{2}\\rfloor$. Moreover, this value is optimal. We then consider the case of strongly $N$-supercyclic operators. An operator $T$ is strongly $N$-supercyclic if $\\mathbb{R}^n$ has an $N$-dimensional subspace whose orbit under $T$ is dense in $\\mathbb{P}_N(\\mathbb{R}^n)$, the $N$-th Grassmannian. We prove that strong $N$-supercyclicity doe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3575","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":""},"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"}