Relationship among several types of sensitivity in general semi-flows
Dynamical Systems
2019-04-09 v1
Abstract
In this paper, we show that there exists a monoid, on which neither the syndetic property nor the dual syndetic property holds, and there exists a strongly mixing semi-flow with this monoid action which does not have thick sensitivity, syndetic sensitivity, thickly syndetic sensitivity, or thickly periodical sensitivity. Meanwhile, we show that there exists a thickly sensitive cascade which is not multi-sensitive. The first result answers positively Question 2, and the first and the second results answer negatively Question 3 in [A. Miller, A note about various types of sensitivity in general semiflows, Appl. Gen. Topol., 2018].
Keywords
Cite
@article{arxiv.1904.03663,
title = {Relationship among several types of sensitivity in general semi-flows},
author = {Xinxing Wu and Xu Zhang},
journal= {arXiv preprint arXiv:1904.03663},
year = {2019}
}