Dynamics of tuples of matrices in Jordan form

Details Dynamics of tuples of matrices in Jordan form Dynamics of tuples of matrices in Jordan form

2010-03-27

arxiv.org/abs/1003.5321v3

Mathematics

Functional Analysis

28 pages, final version; incorporates the corrections and improvements of the anonymous referee. Numbering has changed, all pa

Scientific paper

A tuple (T_1,...,T_k) of (n x n) matrices over R is called hypercyclic if for
some x in R^n the set {T^{m_1} T^{m_2}...T^{m_k} x : m_1,m_2,...,m_k in N} is
dense in R^n. We prove that the minimum number of (n x n) matrices in Jordan
form over R which form a hypercyclic tuple is n+1. This answers a question of
Costakis, Hadjiloucas and Manoussos.

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