A note on the sensitivity of semiows
Dynamical Systems
2019-04-08 v1
Abstract
In this note, it is shown that there exist two non-syndetically sensitive cascades defined on complete metric spaces whose product is syndetically sensitive, answering negatively the Question 9.2 posed in [12, Miller, A., Money, C., Turk. J. Math., 41 (2017): 1323{1336]. Moreover, it is shown that there exists a syndetically sensitive semiflow (G;X) defined on a complete metric space X such that (G1;X) is not sensitive for some syndetic closed submonoid G1 of G, answering negatively the Open question 3 posed in [13, Money, C., PhD thesis, University of Louisville, 2015] and Question 43 posed in [8, Miller, A., Real Anal. Exchange, 42 (2017): 9{24].
Cite
@article{arxiv.1904.02864,
title = {A note on the sensitivity of semiows},
author = {Xinxing Wu and Xin Ma and Guanrong Chen and Tianxiu Lu},
journal= {arXiv preprint arXiv:1904.02864},
year = {2019}
}