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Relationship among several types of sensitivity in general semi-flows

  • Xinxing Wu
  • Xu ZhangEmail author
Research Article
  • 16 Downloads

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 (Miller in Appl Gen Topol 19:281–289, 2018).

Keywords

Semi-flow Topological monoid Sensitivity 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11601449 and 11701328), the Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications (No. 18TD0013), Youth Science and Technology Innovation Team of Southwest Petroleum University for Nonlinear Systems (No. 2017CXTD02), Shandong Provincial Natural Science Foundation, China (Grant ZR2017QA006), Young Scholars Program of Shandong University, Weihai (No. 2017WHWLJH09), and the Fundamental Research Funds for the Central Universities (No. 2019ZRJC005).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of SciencesSouthwest Petroleum UniversityChengduPeople’s Republic of China
  2. 2.Institute for Artificial Intelligence, Southwest Petroleum UniversityChengduPeople’s Republic of China
  3. 3.Department of MathematicsShandong UniversityWeihaiPeople’s Republic of China

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