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Mathematical Communications, Vol. 29 No. 1, 2024.

Original scientific paper

Dynamical Behaviours of Some Horseshoe-like Maps on Cantor Dust C × C

Saliha Şeker, ; Eskisehir Technical University, Department of Mathematics, Eskisehir, Turkey *
Mustafa Saltan ; Eskisehir Technical University, Department of Mathematics, Eskisehir, Turkey

* Corresponding author.

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Abstract

Dynamical systems are one of the important research topics that have applications in many disciplines. In particular, investigating whether a dynamical system is chaotic gives us important information about the dynamical system. In this paper, some dynamical systems are defined on Cantor dust C × C by inspiring of the construction of Smale’s horseshoe map. We also express these dynamical systems via ternary numbers and compute their periodic points. Then we show that they are chaotic in the sense of Devaney. Finally, we compare these dynamical systems according to topologically equivalent or not.

Keywords

Cantor dust; Smale’s horseshoe map; chaos; periodic points; topological conjugacy

Hrčak ID:

315323

URI

https://hrcak.srce.hr/315323

Publication date:

19.3.2024.

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