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Dynamics of tuples of matrices

Authors: G. Costakis, D. Hadjiloucas and A. Manoussos
Journal: Proc. Amer. Math. Soc. 137 (2009), 1025-1034
MSC (2000): Primary 47A16
Published electronically: October 17, 2008
MathSciNet review: 2457443
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Abstract: In this article we answer a question raised by N. Feldman in 2008 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, \dotsc ,A_n)$ of $ n\times n$ matrices over $ \mathbb{R}$ such that $ (A_1, A_2, \ldots ,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.

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Additional Information

G. Costakis
Affiliation: Department of Mathematics, University of Crete, Knossos Avenue, GR-714 09 Heraklion, Crete, Greece

D. Hadjiloucas
Affiliation: Department of Computer Science and Engineering, European University Cyprus, 6 Diogenes Street, Engomi, P.O. Box 22006, 1516 Nicosia, Cyprus

A. Manoussos
Affiliation: Fakultät für Mathematik, SFB 701, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

Keywords: Hypercyclic operators, tuples of matrices.
Received by editor(s): March 24, 2008
Published electronically: October 17, 2008
Additional Notes: During this research the third author was fully supported by SFB 701 “Spektrale Strukturen und Topologische Methoden in der Mathematik” at the University of Bielefeld, Germany. He would also like to express his gratitude to Professor H. Abels for his support.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society