Dynamical Analysis on the Discrete Pentagon Fractal

Nisa Aslan

Vol. 29 No. 2 (2024)

Regular Articles

Dynamical Analysis on the Discrete Pentagon Fractal

Published 2024-10-04

Nisa Aslan

Nisa Aslan
Department of Mathematics, Eskisehir Technical University

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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

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