Overview: 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 similari.The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time
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