Linear Dynamical Systems

Abstract

This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, $\mathcal{U}$-frequent hypercyclicity, reiterative hypercyclicity, operators of C-type, Li-Yorke and distributional chaos, and hypercyclic algebras.

Survey invited by Bulletin of the Irish Mathematical Society. Version accepted for publication

References in corpus (6)

• Strong mixing measures for linear operators and frequent hypercyclicity
• Existence of common hypercyclic vectors for translation operators
• Hypercyclicity Properties of Commutator Maps
• Common hypercyclic vectors for high dimensional families of operators
• A bridge between U-frequent hypercyclicity and frequent hypercyclicity
• Hypercyclic Algebras for convolution operators of unimodular constant term

Cited by in corpus (5)

• Recurrent subspaces in Banach spaces
• Shifts on trees versus classical shifts in chain recurrence
• Entropy, pressure, ground states and calibrated sub-actions for linear dynamics
• Interactions between Universal Composition Operators and Complex Dynamics
• Interval-valued estimation for discrete-time linear systems: application to switched systems