21808 articles – 15604 Notices  [english version]
 HAL : hal-00697603, version 2
 arXiv : 1205.3575
 Versions disponibles : v1 (15-05-2012) v2 (16-05-2012)
 $n$-supercyclic and strongly $n$-supercyclic operators in finite dimension
 (10/05/2012)
 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 does not occur non-trivially in finite dimension.
 1 : Laboratoire de Mathématiques CNRS : UMR6620 – Université Blaise Pascal - Clermont-Ferrand II
 Domaine : Mathématiques/Analyse fonctionnelle
 Mots Clés : n-supercyclicity – n-supercyclic operators – strong n-supercyclicity – strongly n-supercyclic operators – Jordan decomposition – finite dimension – supercyclic operators
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 hal-00697603, version 2 http://hal.archives-ouvertes.fr/hal-00697603 oai:hal.archives-ouvertes.fr:hal-00697603 Contributeur : Romuald Ernst <> Soumis le : Mardi 15 Mai 2012, 17:45:37 Dernière modification le : Mercredi 16 Mai 2012, 08:54:30