Comparison of some dynamical systems on the quotient space of the Sierpinski tetrahedron

In this paper, it is aimed to construct two different dynamical systems on the Sierpinski tetrahedron. To this end, we consider the dynamical systems on a quotient space of $\{ 0,1,2,3 \}^{\mathbb{N}}$ by using the code representations of the points on the Sierpinski tetrahedron. Finally, we compare the periodic points to investigate topological conjugacy of these dynamical systems and we conclude that they are not topologically equivalent.