Investigation of chaotic dynamical systems on discrete sierpinski triangle

Chaotic dynamical systems are an important tool for understanding the complexity of many events in nature that encounter even in our daily lives. The basin of attraction of these systems are sometimes expressed with fractal models. For this reason, there is a natural relationship between fractals and chaos. In addition, different chaotic dynamical systems can be defined using the structure of the relevant fractal. In this thesis, firstly, the code representations compatible with the iterated function systems (IFS) of the points on discrete Sierpinski triangle which is a totally disconnected fractal, are determined. Then, a family of dynamical systems on the discrete Sierpinski triangle is obtained by using the combination of the elements of S_3, which is the symmetry group of equilateral triangle, with the shift map. Also, the periodic points of these systems defined on S^d are given in a general form. Thus, we show that these maps are chaotic in the sense of Devaney and then topological equivalances between these systems are investigated. In the last part of the thesis, different dynamical systems are defined using folding and expansion maps. Also, it is examined whether some dynamical systems in the family obtained by the combination of the shift map and the elements of the symmetry group of S_3 are topologically equivalent to the dynamical systems which are defined in last section.