Original scientific paper

Dynamical Analysis on the Discrete Pentagon Fractal

Nisa Aslan orcid.org/0000-0002-2103-0511 ; Department of Mathematics, Eskisehir Technical University, Eskisehir, TURKEY *

* Corresponding author.

Abstract

In this study, we aim to define a chaotic dynamical system family on a discrete pentagon fractal, \(P^{d}\), a totally disconnected fractal set. One of the way to define dynamical systems on the discrete n-flake fractal is to use the elements of its symmetry group. Thus, by the help of the elements of the symmetry group of equilateral pentagon \(D_{5}\) and the shift map (\(\sigma\)), we obtain different dynamical systems via the code representations of the points on \(P^{d}\). Moreover, we investigate Devaney's chaos conditions for this family of dynamical systems.

Keywords

Chaotic dynamical systems; topological conjugacy; discrete pentagon fractal; symmetry groups

Hrčak ID:

321271

URI

https://hrcak.srce.hr/321271

Publication date:

7.10.2024.

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