Dynamics of tuples of matrices

In this article we answer a question raised by N. Feldman in \cite{Feldman} concerning the dynamics of tuples of operators on \(\mathbb{R}^n\). In particular, we prove that for every positive integer \(n\geq 2\) there exist \(n\) tuples \((A_1, A_2, ..., A_n)\) of \(n\times n\) matrices over \(\math...

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Bibliographic Details
Published in:arXiv.org 2008-03
Main Authors: Costakis, George, Hadjiloucas, Demetris, Manoussos, Antonios
Format: Article
Language:English
Subjects:
Jordan form
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Summary:In this article we answer a question raised by N. Feldman in \cite{Feldman} concerning the dynamics of tuples of operators on \(\mathbb{R}^n\). In particular, we prove that for every positive integer \(n\geq 2\) there exist \(n\) tuples \((A_1, A_2, ..., A_n)\) of \(n\times n\) matrices over \(\mathbb{R}\) such that \((A_1, A_2, ..., A_n)\) is hypercyclic. We also establish related results for tuples of \(2\times 2\) matrices over \(\mathbb{R}\) or \(\mathbb{C}\) being in Jordan form.
ISSN:2331-8422