SOME THEOREMS ON TOPOLOGICAL TRANSITIVITY AND PERIODIC POINTS OF TOPOLOGICAL DYNAMICAL SYSTEMS


By

Shabani Makwaru¹ , Santosh Kumar² and Marco Mpimbo

¹,³Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Tanzania-35062 

²Department of Mathemtics, School of Physical Sciences North Eastern Hill University, Shillong, Meghalaya, India-793022 

Email: makwaruudsm@gmail.com, drsengar2002@gmail.com, kmpimbo33@gmail.com 

(Received: March 15, 2024; In format: April 01, 2024; Revised: June 15, 2024; Accepted: June 17, 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54139



Abstract

Topological transitivity is a key characteristic of a topological dynamical system (X, T). In this article, we discuss some connections between topological transitivity and periodic points. Also, the results due to Vellekoop and Berglund [12] are extended in this work. 


2020 Mathematical Sciences Classification: 47A16, 47A15. 

Keywords and Phrases: Topological dynamical system, Topological transitivity, Minimality, Dense orbit, Periodic point, Sensitivity, Chaotic system. 

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