This book systematically presents a theory for the mapping switchability of discontinuous, discrete dynamical systems. In discontinuous discrete systems, there are a set of distinct mappings in ditinct domains. Thus, the problems are how distinct mapping actions can crossover the boundary and get into other domains with mapping switch, and what conditions for the mapping switchability at the boundary can exist in such discontinuous dynamical systems. In this book, the mapping swithcbaility theory is developed, the fully separable and swappable source mapping actions are described, and the switchable and returnable mapping actions are defined as well. The mapping barriers at the boundary are introduced for the source mapping actions and switchable and returnable mapping actions. Finally, the mapping switchability theory to the edge is developed. Using such theory, the Cantor sets and Smale horseshoe sets in topology dynamics can be easily explained.
- Introduced mapping switchability
- Developed mapping switchability and singularity theory
- Presented separable and swappable source mapping actions,
- Presented switchable and returnable mapping actions
- Developed the theory of mapping barriers
- Discussed mapping switchability and attractivity to the edges
- Easy to read
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