Chapter 2: Introduction to Fractal Dynamics

In this chapter, in order to get a deeper understanding of nonlinear dynamical phenomena covered by this book, the fundamental concepts of one-dimensional (1D) maps and fractal sets are briefly reviewed and illustrated. First notions of Cantor's set, Cantor's dust and Koch's snowflake are presented. Then 1D maps are considered putting emphasis on their regular and chaotic dynamics, the cobweb diagrams and the period doubling bifurcation routes to chaos including estimation of the Feigenbaum constant are also briefly revisited. The Sharkovsky theorem is addressed with presentation of its advantages and limitations. Next, the Julia, Fabout and Mandebrot sets are shortly described and illustrated.