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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 5, pp 1431–1441 | Cite as

Alterations and Rearrangements of a Non-autonomous Dynamical System

  • Manish Raghav
  • Puneet SharmaEmail author
Original Paper

Abstract

In this paper, we discuss the dynamics of alterations and rearrangements of a non-autonomous dynamical system generated by the family \({\mathbb {F}}\). We prove that while insertion/deletion of a map in the family \({\mathbb {F}}\) can disturb the dynamics of a system, the dynamics of the system does not change if the map inserted/deleted is feeble open. In the process, we prove that if the inserted/deleted map is feeble open, the altered system exhibits any form of mixing/sensitivity if and only if the original system exhibits the same. We extend our investigations to properties like equicontinuity, minimality, and proximality for the two systems. We prove that any finite rearrangement of a non-autonomous dynamical system preserves the dynamics of original system if the family \({\mathbb {F}}\) is feeble open. We also give examples to show that the dynamical behavior of a system need be not be preserved under infinite rearrangement.

Keywords

Non-autonomous dynamical systems Equicontinuity Transitivity Sensitivity Proximality 

Mathematics Subject Classification

37B20 37B55 54H20 

Notes

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Department of MathematicsI.I.T. JodhpurJodhpurIndia

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