English

Multiple recurrence and hypercyclicity

Functional Analysis 2021-06-08 v2

Abstract

We study multiply recurrent and hypercyclic operators as a special case of F\mathcal F-hypercyclicity, where F\mathcal F is the family of subsets of the natural numbers containing arbitrarily long arithmetic progressions. We prove several properties of hypercyclic multiply recurrent operators, we characterize those operators which are weakly mixing and multiply recurrent, and we show that there are operators that are multiply recurrent and hypercyclic but not weakly mixing.

Keywords

Cite

@article{arxiv.2104.15033,
  title  = {Multiple recurrence and hypercyclicity},
  author = {Rodrigo Cardeccia and Santiago Muro},
  journal= {arXiv preprint arXiv:2104.15033},
  year   = {2021}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2003.07161