Examination of the Topological Conjugacy of Dynamical Systems on the Box Fractal

Abstract

In this paper, we examine dynamical systems obtained with the same expanding and different numbers of folding transformations on the Box fractal $(B)$. We express these dynamical systems through the addresses of points  by using the terms of $\{0,1,2,3,4\}$.  We then compute and compare the periodic points of the dynamical systems. Finally, we examine these systems in the sense of topological conjugacy (equivalence) and we investigate the chaos conditions for the dynamical systems.