COMPLEX DYNAMICS - ADVANCED SYSTEM DYNAMICS IN COMPLEX VARIABLES

This graduate-level text offers a comprehensive introduction to the methods and techniques of modern complex-valued, nonlinear dynamics and its various physical and non-physical applications. Readers learn to predict and control low- and high-dimensional as well as continuous- and discrete-time nonlinear systems dynamics in complex variables.Following an introductory chapter, Chapter 2 develops low-dimensional dynamics in the complex plane, theoretical and computational, and continuous- and discrete-time. Chapter 3 presents quantum dynamics, mainly following Dirac's notation. Chapter 4 develops geometrical machinery of complex manifolds. Chapter 5 discusses high-dimensional complex continuous dynamics, and Chapter 6 explores the formalism of complex path integrals.In the final chapter, all previously developed methods are employed to present the "Holy Grail" of modern physical and cosmological science, the search for the "theory of everything" and the "true" cosmological dynamics. In short, this is a serious scientific tool that enables you to perform top-level research in modern complex-valued nonlinear dynamics.