Creating a new family of dynamic system on 2-dimensional Cantor set

Dynamic systems play an important role in mathematics and in many areas where they find application. Whether a dynamic system is chaotic or not is a very important character for the system. Although many chaotic dynamical systems have been studied in detail in the literature, it has been observed that this concept has begun to be studied extensively on self-similar similar sets in recent years. Some discrete dynamical systems have been defined using different methods on some classical self-similar sets such as the Cantor set and the Sierpinski triangle, and it is investigated whether these systems are chaotic or not. In this thesis, new discrete dynamical systems are constructed on the 2-dimensional Cantor set, also known as Cantor dust in the plane, using the code representations of the points, and it is examined in detail whether these dynamical systems are chaotic or not. On the other hand, a discrete dynamical system naturally determines a stochastic process. In the last part of this thesis, it has been investigated the stochastic processes determined by these new discrete dynamical systems defined on the 2-dimensional Cantor set.