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It is well known that the theory of dynamical systems is an essential mathematical tool in the analysis of various real-world processes and phenomena that evolve over time. Different aspects of this rich field of research are evolving all the time, including new theoretical results for qualitative investigation as well as fast numerical techniques for approximate solution. The book provides an overview of the current state of the art in this fascinating and critically important field of pure and applied mathematics, presenting recent developments in theory, modeling, algorithms, and applications.