On the minimal number of matrices which form a locally hypercyclic, non-hypercyclic tuple

DOI10.1016/j.jmaa.2009.10.020zbMath1200.47014arXiv0904.3142OpenAlexW2082407767MaRDI QIDQ847770

Demetris Hadjiloucas, George Costakis, Antonios Manoussos

Publication date: 19 February 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.3142

zbMATH Keywords

hypercyclic operators\(J\)-class operatorslocally hypercyclic operatorstuples of matrices

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Cyclic vectors, hypercyclic and chaotic operators (47A16) Special matrices (15B99)

Related Items (17)

Hypercyclic abelian semigroups of matrices on \(\mathbb{R}^n\) ⋮ On supercyclicity for abelian semigroups of matrices on ℝ^n ⋮ Unnamed Item ⋮ J-class abelian semigroups of matrices on ℝ ⁿ ⋮ Supercyclic abelian semigroups of matrices on \(\mathbb C^n\) ⋮ Dynamical classification for complex matrices ⋮ Topological generators of Abelian Lie groups and hypercyclic finitely generated Abelian semigroups of matrices ⋮ Subspace-hypercyclic abelian semigroups of matrices on \(\mathbb{R}^n\) ⋮ \(n\)-weakly supercyclic matrices ⋮ Abelian Semigroups of Matrices on ℂⁿ and Hypercyclicity ⋮ Topologically transitive semigroup actions of real linear fractional transformations ⋮ Chaotic behavior of discrete-time linear inclusion dynamical systems ⋮ J-class abelian semigroups of matrices on \(\mathbb C^n\) and hypercyclicity ⋮ Subspace-hypercyclic abelian linear semigroups ⋮ Semigroups of matrices with dense orbits ⋮ Coarse topological transitivity on open cones and coarsely \(J\)-class and \(D\)-class operators ⋮ Hypercyclic abelian semigroups of affine maps on \(\mathbb{C}^{n}\)

Cites Work

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• \(J\)-class weighted shifts on the space of bounded sequences of complex numbers
• Report 37/2006: Mini-workshop: Hypercyclicity and linear chaos (August 13th -- August 19th, 2006)
• Hypercyclic tuples of operators and somewhere dense orbits
• Hypercyclic pairs of coanalytic Toeplitz operators
• The range of operators on von Neumann algebras
• Semigroups of matrices with dense orbits
• J-class operators and hypercyclicity
• Dynamics of tuples of matrices

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