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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.3575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-16T06:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"2ea189bbee09194ae0b5145f2750d47d37ba8f3c6ce4daf0fbecadb92a80ee61","abstract_canon_sha256":"18d66a5e290cb72cc15c9d21a6c15420b005bbddb7a4fbc703bbc98fc6eb13dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:21.352487Z","signature_b64":"tYaQx6gqvO+e0QBbxZGuDmy5NOxXKBAWjuoSesgHJ2j++8Th7i8pnQm1niHAoKitL76sekjc4y9t+VVcnu1ODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b66a60bd08237c5c3ce5070cd1dc86cb807b53a7ef532c844bf7e0013e0d6481","last_reissued_at":"2026-05-18T03:03:21.351941Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:21.351941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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