Linear Dynamical Systems
arXiv:2007.12647 · doi:10.33232/BIMS.0086.47.78
Abstract
This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, -frequent hypercyclicity, reiterative hypercyclicity, operators of C-type, Li-Yorke and distributional chaos, and hypercyclic algebras.
arXiv commentSurvey invited by Bulletin of the Irish Mathematical Society. Version accepted for publication
References in corpus (19)
- The unconditional basic sequence problem
- Difference sets and frequently hypercyclic weighted shifts
- Recurrence properties of hypercyclic operators
- Mean Li-Yorke chaos in Banach spaces
- Strong transitivity properties for operators
- Strong mixing measures for linear operators and frequent hypercyclicity
- A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces
- Inverse of frequently hypercyclic operators
- A quantitative interpretation of the frequent hypercyclicity criterion
- Existence of common hypercyclic vectors for translation operators
- Algebrable sets of hypercyclic vectors for convolution 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 and composition operators
- Rate of Growth of Distributionally Chaotic Functions
- Dynamics of Generalised Derivations and Elementary Operators
- Hypercyclic Algebras for convolution operators of unimodular constant term
- Existence of common and upper frequently hypercyclic subspaces
Cited by in corpus (6)
- Weighted composition operators on Fock spaces and their dynamics
- 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