Remarks on sensitivity and chaos in nonautonomous dynamical systems

Abstract

In this article, we show that (1) there exists a nonautonomous system which is sensitive with dense minimal points but not syndetically sensitive; (2) there exists a nonautonomous system which is syndetically transitive but not syndetically sensitive; (3) there exists a ${\mathcal{F}}_s$-transitive nonautonomous system with two different minimal subsets and not ${\mathcal{F}}_{ts}$-sensitive. These examples disprove Theorem 2, one part of Theorem 4 and Theorem 10 proved by Li and Wang [Sensitivity and chaoticity on nonautonomous dynamical systems, Int. J. Bifur. Chaos 30 (2020), 11 pp., Article 2050146].

Keywords:

• Nonautonomous dynamical system
• sensitivity
• chaos
• transitivity

AMS CLASSIFICATIONS:

• Primary 37B55
• 54H20
• Secondary 54B20

Acknowledgments

The authors express their sincere gratitude to the referee for his/her valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author is supported by the Ministry of Minority Affairs, Government of India, Maulana Azad National Fellowship (F.No. 61-1/2019(SA-III)).