Chaotic dynamical systems on the Sierpinski gasket and the Sierpinski tetrahedron

In this thesis, it is aimed to construct chaotic dynamical systems on the Sierpinski gasket and the Sierpinski tetrahedron from the classical fractals. In the first part of this study, basic definitions about fractals and dynamical systems are given. In the second part, escape time algorithm is mentioned and examples of Barnsley's studies are examined. By using maps which are different from the maps defined by Barnsley, classical and right Sierpinski gaskets are obtained via escape time algorithm and these fractals are drawn by Maple programme. In the other part of this study, discrete chaotic dynamical systems are obtained on two and three dimensional Sierpinski gasket. An intrinsic metric formula is defined on the Sierpinski tetrahedron and a geometrical property of this metric is examined. Moreover, periodic points and the conditions of being chaotic of these dynamical systems, defined on the Sierpinski gasket and Sierpinski tetrahedron, are investigated. In addition, different dynamical systems on the same structures are compared. Finally, a generalized intrinsic metric formula and a dynamical system example on the n-dimensional Sierpinski gasket are given.