Abelian Semigroups of Matrices on ℂn and Hypercyclicity
Abelian Semigroups of Matrices on ℂn and Hypercyclicity
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DOI：
10.1017/s0013091513000539
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发表时间：
2013-09
影响因子：
0.7
通讯作者：
A. Ayadi;H. Marzougui
中科院分区：
文献类型：
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作者：
A. Ayadi;H. Marzougui
本文给出了n上超循环交换矩阵半群的一个完整刻画。对于n-生成半群，这个特征是明确的，它被用来确定在n-上形成n-超循环交换半群的标准形矩阵的最小数目。特别地，我们证明了由n个矩阵生成的交换半群不可能是超循环的。
Abstract We give a complete characterization of a hypercyclic abelian semigroup of matrices on ℂn. For finitely generated semigroups, this characterization is explicit and it is used to determine the minimal number of matrices in normal form over ℂ that form a hypercyclic abelian semigroup on ℂn. In particular, we show that no abelian semigroup generated by n matrices on ℂn can be hypercyclic.