Arithmetic progressions and chaos in linear dynamics
Functional Analysis
2020-11-17 v4
Abstract
We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. To achieve this, we study -hypercyclicity for a family of subsets of the natural numbers associated with the existence of arbitrarily long arithmetic progressions. We investigate their connection with different concepts in linear dynamics.
Cite
@article{arxiv.2003.07161,
title = {Arithmetic progressions and chaos in linear dynamics},
author = {Rodrigo Cardeccia and Santiago Muro},
journal= {arXiv preprint arXiv:2003.07161},
year = {2020}
}