Multiple recurrence and hypercyclicity
Functional Analysis
2021-06-08 v2
Abstract
We study multiply recurrent and hypercyclic operators as a special case of -hypercyclicity, where 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.
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