English

Strong topological transitivity, hypermixing, and their relationships with other dynamical properties

Functional Analysis 2023-04-06 v1

Abstract

Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger version of the mixing property. We continue the investigation of these notions with two main results. First, we show there are dynamical systems which are strongly topologically transitive but not weakly mixing. We then show that on p\ell^p or c0c_0, there is a weighted backward shift which is strongly topologically transitive but not mixing.

Keywords

Cite

@article{arxiv.2304.02073,
  title  = {Strong topological transitivity, hypermixing, and their relationships with other dynamical properties},
  author = {Ian Curtis and Sean Griswold and Abigail Halverson and Eric Stilwell and Sarah Teske and David Walmsley and Shaozhe Wang},
  journal= {arXiv preprint arXiv:2304.02073},
  year   = {2023}
}