Complex Dynamics

Complex Dynamics: Advanced System Dynamics in Complex Variables is a graduate-level monographic textbook. It has seven Chapters. The introductory Chapter 1 explains ‘in plain English’ the objective of the book and provides the preliminaries in complex numbers and variables; it also gives a soft introduction to quantum dynamics. Chapter 2 develops low-dimensional dynamics in the complex plane, theoretical and computational, continuous- and discrete-time. Chapter 3 presents a modern introduction to quantum dynamics, mainly following Dirac's notation. Chapter 4 develops geometrical machinery of complex manifolds, essential for the further text. Chapter 5 develops high-dimensional complex continuous dynamics, which takes place on complex manifolds. Chapter 6 develops the formalism of complex path integrals, which extends the continuous dynamics to the general high-dimensional dynamics, which can be both discrete and stochastic. In the last, Chapter 7, 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.