ABSTRACT
This chapter explores dynamical systems that exhibited some properties. It starts with the cantor middle-thirds set that exemplifies the fractal structure that often accompanies chaotic dynamics. Next, the chapter introduce a function called the shift map that captures the essence of the dynamics. The chapter uses the of the cantor set to construct a new function that puts the dynamics of the given dynamical system into correspondence with the dynamics of the shift map. The construction of the classic cantor middle-thirds set is an iterative process that begins with the closed interval. In the first step of the construction, remove the middle-third open interval. The next step is to remove the open middle-thirds of each of intervals.
