# A note on the sensitivity of semiows

## TL;DR

This paper investigates the properties of syndetic sensitivity in dynamical systems, providing counterexamples that challenge previous assumptions and answering open questions in the field.

## Contribution

It constructs specific examples of dynamical systems that demonstrate unexpected behaviors of syndetic sensitivity, addressing open questions from prior research.

## Key findings

- Existence of non-syndetically sensitive cascades with syndetically sensitive products.
- Existence of syndetically sensitive semiflows with non-sensitive submonoids.

## 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].