Dynamics of tuples of matrices in Jordan form
Functional Analysis
2013-10-14 v3 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.1003.5321,
title = {Dynamics of tuples of matrices in Jordan form},
author = {George Costakis and Ioannis Parissis},
journal= {arXiv preprint arXiv:1003.5321},
year = {2013}
}
Comments
28 pages, final version; incorporates the corrections and improvements of the anonymous referee. Numbering has changed, all paragraph counters after the first are increased by +1. Several typos corrected. Lemma 4.7 and Corollary 4.10 now have detailed proofs. The proof of Lemma 6.4 has been rewritten for clarity. To appear in Oper. Matrices