This book details prediction and control of high–dimensional chaotic and attractor systems of real life. It provides a scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics. Coverage details Smale’s topological transformations of stretching, squeezing and folding and Poincaré's 3-body problem and basic techniques of chaos control. It offers a review of both Landau’s and topological phase transition theory as well as Haken’s synergetics and deals with phase synchronization in high-dimensional chaotic systems. In addition, the book presents high-tech Josephson junctions, deals with fractals and fractional Hamiltonian dynamics, and offers a review of modern techniques for dealing with turbulence. It also offers a brief on the cutting edge techniques of the high-dimensional nonlinear dynamics (including geometries, gauges and solitons, culminating into the chaos field theory).