Chaotic functions in sense of Devaney

There are various definitions of a chaotic function in the theory of discrete dynamical systems. The Devaney's definition of chaos is the most popular one among the mathematicians. Devaney's definition is consist of three main ingredients. Namely, density of periodic points, topological transitivity and sensitive dependence on initial conditions which are called the chaos conditions. In this work we give examples of chaotic functions in the sense of Devaney. Firstly we list the well known examples such as Logistic map, Tent map and Shift map. We study on the Shift map in details. We point out some relationships between chaos conditions and alter native conditions to chaos conditions. In the main body of this work we obtain chaotic functions in higher dimensional spaces by using product tecnique. We also construct chaotic functions on n-dimensional unit disc by using the topological conjugacy argument. In the last chapter we discuss chaotic functions in general topological spaces.