若尔当型矩阵组的动力学
泛函分析
2013-10-14 v3 动力系统
摘要
如果对于 R 上的某些 x 属于 R^n，集合 {T_1^{m_1} T_2^{m_2}...T_k^{m_k} x : m_1,m_2,...,m_k 属于 N} 在 R^n 中稠密，则 R 上的 (n x n) 矩阵组 (T_1,...,T_k) 被称为超循环的。我们证明了 R 上构成超循环组的若尔当型 (n x n) 矩阵的最小数目为 n+1。这回答了 Costakis、Hadjiloucas 和 Manoussos 的一个问题。
引用
@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}
}
备注
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