"Complex Dynamics: Advanced System Dynamics in Complex Variables" by Vladimir G. Ivancevic and Tijana T. Ivancevic

This book is a graduate-level monographic textbook. It is designed as a comprehensive introduction into methods and techniques of modern complex-valued nonlinear dynamics with its various physical and non-physical applications.

This monograph is devoted to understanding, prediction and control of both low- and high-dimensional, as well as both continuous- and discrete-time, nonlinear systems dynamics in complex variables. Its objective is to provide a serious reader with a serious scientific tool that will enable him/her to actually perform a competitive research in modern complex-valued nonlinear dynamics.

Contents
1 Introduction
1.1 Why Complex Dynamics?
1.2 Preliminaries: Basics of Complex Numbers and Variables
1.3 Soft Introduction to Quantum Dynamics
2 Nonlinear Dynamics in the Complex Plane
2.1 Complex Continuous Dynamics
2.2 Complex Chaotic Dynamics: Discrete and Symbolic
3 Complex Quantum Dynamics
3.1 Non-Relativistic Quantum Mechanics
3.2 Relativistic Quantum Mechanics and Electrodynamics
4 Complex Manifolds
4.1 Smooth Manifolds
4.2 Complex Manifolds
4.3 Basics of Kahler Geometry
4.4 Conformal Killing-Riemannian Geometry
4.5 Stringy Manifolds
5 Nonlinear Dynamics on Complex Manifolds
5.1 Gauge Theories
5.2 Monopoles
5.3 Hermitian Geometry and Complex Relativity
5.4 Gradient Kahler Ricci Solitons
5.5 Monge-Ampere Equations
5.6 Quantum Mechanics Viewed as a Complex Structure on a Classical Phase Space
5.7 Geometric Quantization
5.8 K-Theory and Complex Dynamics
5.9 Self-Similar Liouville Neurodynamics
6 Path Integrals and Complex Dynamics
6.1 Path Integrals: Sums Over Histories
6.2 Complex Dynamics of Quantum Fields
6.3 Complex Stringy Dynamics
6.4 Other Applications of Path Integrals
7 Quantum Gravity and Cosmological Dynamics
7.1 Search for Quantum Gravity
7.2 Loop Quantum Gravity
7.3 Cosmological Dynamics
References
Index