Abelian Semigroups of Matrices on ℂn and Hypercyclicity. Issue 2 (5th September 2013)

• Record Type: Journal Article
• Authors: Ayadi, Adlene; Marzougui, Habib
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 57:Issue 2(2014)
• Page Start: 323
• Page End: 338
• Publication Date: 2013-09-05
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091513000539
• Languages: English
• ISSNs: 0013-0915

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>We give a complete characterization of a hypercyclic abelian semigroup of matrices on ℂ^{<italic>n</italic>}. 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 ℂ^{<italic>n</italic>}. In particular, we show that no abelian semigroup generated by <italic>n</italic> matrices on ℂ^{<italic>n</italic>} can be hypercyclic.</p> </abstract>