Sensitivity and chaos on product and on hyperspatial semiflows

ABSTRACT

We study stronger forms of sensitivity on the arbitrary product of semiflows on Hausdorff uniform spaces. Moreover, Devaney chaos, Poincaré chaos, and their related properties are studied on product semiflows. Furthermore, we study relations between the chaos-related properties of a semiflow and that of its induced hyperspatial semiflow. Some results regarding stronger forms of sensitivity are also obtained on hyperspatial semiflows.

Keywords:

• Semiflow
• sensitivity
• Devaney chaos
• Poincaré chaos
• hyperspace

MSCs(2020):

• Primary 37B05
• 37C10
• Secondary 37B99
• 37D45

Acknowledgments

Authors are thankful to the referees for their valuable comments and suggestions for improvement of the paper. The first author is funded by CSIR-SRF Sr.No. 1121641416 Ref.No: 18/12/2016(ii) EU-V (File No: 09/045(1532)/2017-EMR-I).

Disclosure statement

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

Additional information

Funding

The first author is funded by CSIR-SRF Sr.No. 1121641416 Ref.No: 18/12/2016(ii) EU-V (File No: 09/045(1532)/2017-EMR-I).