Non-recurrence sets for weakly mixing linear dynamical systems
Dynamical Systems
2019-02-20 v1 Functional Analysis
Abstract
We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space when endowed with a non-degenerate Gaussian measure. We generalize some recent results of Bergelson, del Junco, Lema\'nczyk and Rosenblatt, and show in particular that sets \{n_k\} such that n_{k+1}/{n_k} tends to infinity, or such that n_{k} divides n_{k+1} for each k, are non-recurrence sets for weakly mixing linear dynamical systems. We also give examples, for each r, of r-Bohr sets which are non-recurrence sets for some weakly mixing systems.
Cite
@article{arxiv.1202.3114,
title = {Non-recurrence sets for weakly mixing linear dynamical systems},
author = {Sophie Grivaux},
journal= {arXiv preprint arXiv:1202.3114},
year = {2019}
}