5 papers
Chain recurrent shifts on trees
Andrew Mortensen, David Walmsley
We characterize when a weighted backward shift is chain recurrent on the () and spaces of a directed tree. The characterization is given in terms of…
Ultra hypercyclicity and its connection to mixing properties
Martin Liu, David Walmsley, James Xue
Recently, two new topological properties for operators acting on a topological vector space were introduced: strong hypercyclicity and hypermixing. We introduce a new property call…
Strong topological transitivity, hypermixing, and their relationships with other dynamical properties
Ian Curtis, Sean Griswold, Abigail Halverson +4
Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological trans…
Two Families of Hypercyclic Non-Convolution Operators
Alex Myers, Muhammadyusuf Odinaev, David Walmsley
Let be the set of all entire functions endowed with the topology of uniform convergence on compact sets. Let , let $C_{λ,b}:H(\mathbb{C})\to H(\ma…
Linear Factorization of Hypercyclic Functions for Differential Operators
Kit C. Chan, Jakob Hofstad, David Walmsley
On the Fréchet space of entire functions , we show that every nonscalar continuous linear operator which commutes with differentia…