On the Construction of Chaotic Dynamical Systems on the Box Fractal

N. Aslan; M. Saltan

doi:10.15421/242105

On the Construction of Chaotic Dynamical Systems on the Box Fractal

N. Aslan (Eskişehir Technical University), https://orcid.org/0000-0002-2103-0511
M. Saltan (Eskişehir Technical University), https://orcid.org/0000-0002-3252-3012

Abstract

In this paper, our main aim is to obtain two different discrete chaotic dynamical systems on the Box fractal ($$$B$$$). For this goal, we first give two composition functions (which generate Box fractal and filled-square respectively via escape time algorithm) of expanding, folding and translation mappings. In order to examine the properties of these dynamical systems more easily, we use the intrinsic metric which is defined by the code representation of the points on $$$B$$$ and express these dynamical systems on the code sets of this fractal. We then obtain that they are chaotic in the sense of Devaney and give an algorithm to compute periodic points.

Keywords

Box fractal; code representation; intrinsic metric; chaotic dynamical systems; periodic points; escape time algorithm

MSC 2020

28A80; 51F99

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References

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