Dynamical analysis of some special shift maps on discrete Sierpinski triangle

Özlem Seyhan, Nisa Aslan and Mustafa Saltan

Chaos, Solitons & Fractals, 2024, vol. 178, issue C

Abstract: There is a natural relationship between fractals and chaos. In addition, different chaotic dynamical systems can be defined depending on the structure of the relevant fractal. In this paper, we first define a family of dynamical systems on the discrete Sierpinski triangle by using the composition of the shift map and the elements of S3, which is the group of symmetries of the equilateral triangle, via the code representations of the points. Moreover, we give a general formula to construct different dynamical systems on this fractal. Thus, we obtain a family of dynamical systems which are Devaney chaotic. Finally, we classify these dynamical systems in term of topological conjugacy.

Keywords: Chaos; Periodic points; Discrete Sierpinski triangle; Symmetry groups (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077923012845
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012845

DOI: 10.1016/j.chaos.2023.114382

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().