Dynamics with Chaos and Fractals

Stands as the first book presenting theoretical background on the unpredictable point and mapping of fractals.Introduces the concepts of unpredictable functions, abstract self-similarity, and similarity map.Discusses unpredictable solutions of quasilinear ordinary and functional differential equations.Illustrates new ways to construct fractals based on the ideas of Fatou and Julia. Examines unpredictability in ocean dynamics and neural networks, chaos in hybrid systems on a time scale, and homoclinic and heteroclinic motions in economic models