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Full Description
If we try to describe real world in mathematical terms, we will see that real life is very often a high-dimensional chaos. Sometimes, by 'pushing hard', we manage to make order out of it; yet sometimes, we need simply to accept our life as it is. To be able to still live successfully, we need tounderstand, predict, and ultimately control this high-dimensional chaotic dynamics of life. This is the main theme of the present book. In our previous book, Geometrical - namics of Complex Systems, Vol. 31 in Springer book series Microprocessor- Based and Intelligent Systems Engineering, we developed the most powerful mathematical machinery to deal with high-dimensional nonlinear dynamics. In the present text, we consider the extreme cases of nonlinear dynamics, the high-dimensional chaotic and other attractor systems. Although they might look as examples of complete disorder - they still represent control systems, with their inputs, outputs, states, feedbacks, and stability. Today, we can see a number of nice books devoted to nonlinear dyn- ics and chaos theory (see our reference list). However, all these books are only undergraduate, introductory texts, that are concerned exclusively with oversimpli?ed low-dimensional chaos, thus providing only an inspiration for the readers to actually throw themselves into the real-life chaotic dynamics.
Contents
to Attractors and Chaos.- Smale Horseshoes and Homoclinic Dynamics.- 3-Body Problem and Chaos Control.- Phase Transitions and Synergetics.- Phase Synchronization in Chaotic Systems.- Josephson Junctions and Quantum Engineering.- Fractals and Fractional Dynamics.- Turbulence.- Geometry, Solitons and Chaos Field Theory.
