Complexity and control : towards a rigorous behavioral theory of complex dynamical systems / Vladimir G Ivancevic (Defence Science & Technology Organisation, Australia), Darryn J Reid (Defence Science & Technology Organisation, Australia).

Includes bibliographical references and index.

Print version record.

""Contents""; ""Preface""; ""Acknowledgments""; ""Glossary of Frequently Used Symbols""; ""1 Introduction""; ""2 Local Geometrical Machinery for Complexity and Control""; ""2.1 Introduction: Why Kahler Manifolds?""; ""2.1.1 Dynamical Prologue: Complex Hamiltonian Dynamics""; ""2.1.2 Unified Behavioral Picture: Kahler Geometrodynamics ""; ""2.2 Complex Manifolds and Their Vector Bundles""; ""2.2.1 Behavioral Dynamics on Complex Plane""; ""Behavioral dynamics in the complex plane C""; ""Holomorphic functions and their differential operators in C""; ""Residues of meromorphic functions in C""

""2.2.2 3D Rotations: Spinors""""2.2.3 Attractor Dynamics on Riemann Surfaces""; ""Why Riemann surfaces?""; ""2.2.4 Complex Manifolds and Vector Bundles ""; ""2.2.5 (Co)Tangent Spaces to the Complex Manifold""; ""2.2.6 Complex Vector Bundles""; ""2.3 From Kalman Systems to Riemann Manifolds""; ""2.4 Basic Kahler Geometry""; ""2.4.1 Essential Kahler Tensors and Cohomology Groups""; ""2.4.2 Global Kahler Geometry""; ""Fano manifolds""; ""Kahler structures""; ""Two Kahler structures and two alternative points of view""; ""2.4.3 Local Kahler Geometry""; ""Symplectic coordinates""

""2.4.4 Invariant Hamiltonian Dynamics on Kahler Manifolds""""2.5 Dynamics on Quaternion-Kahler Manifolds""; ""2.5.1 Quaternion-Kahler Manifolds""; ""2.5.2 Hamiltonian Dynamics on Quaternion-Kahler Manifolds""; ""2.5.3 Lagrangian Dynamics on Quaternion-Kahler Manifolds""; ""2.6 Kahler-Ricci-Flow Framework""; ""2.6.1 Motivation for the Kahler-Ricci Flow""; ""2.6.2 Ricci Flow on a Kahler Manifold""; ""2.6.3 Definition of the Kahler-Ricci Flow""; ""2.6.4 Evolution of the Kahler-Perelman Entropy""; ""2.7 Summary of Kahler-Ricci Geometrical Dynamics""; ""2.8 Appendix""

""2.8.1 Real Banach and Complex Hilbert Spaces""""2.8.2 From Linear to Nonlinear MIMO Control Theory""; ""Kalman�s Linear State-Space Formalism""; ""Basics of Kalman Filtering""; ""Extended (Nonlinear) Kalman Filter""; ""Ensemble Kalman Filter and Nonlinear Estimation""; ""Affine Nonlinear Control System""; ""Lie Derivative and Lie Bracket in Control Theory""; ""Example: Car-Parking Using Lie Brackets""; ""2.8.3 Basic Complexity Geometrodynamics""; ""Basic Tensor Machinery""; ""Tensor Derivatives on Riemannian Manifolds""; ""Covariant Form of Gradient, Divergence, Curl and Laplacian""

""The Absolute Derivative and 3D Curve Geometry""""Covariant state equation""; ""Basic Exterior Machinery""; ""Basic Manifold Machinery""; ""Tensor Fields and Bundles""; ""Basic de Rham Machinery""; ""Exterior Lagrangian Systems""; ""Basic Gauge Fields""; ""Basic Lie Groups and Their Lie Algebras""; ""2.8.4 Advanced Complexity Geometrodynamics""; ""Basic Riemannian-Ricci Machinery""; ""Basic Hamiltonian Machinery""; ""Pontryagin�s Maximum Principle""; ""Affine Control Systems""; ""Basic Hodge Machinery""; ""Basic Applications to Quantum Field Theory""; ""Lie Algebra-Valued Exterior Forms""

The book Complexity and Control: Towards a Rigorous Behavioral Theory of Complex Dynamical Systems is a graduate-level monographic textbook, intended to be a novel and rigorous contribution to modern Complexity Theory. This book contains 11 chapters and is designed as a one-semester course for engineers; applied and pure mathematicians; theoretical and experimental physicists; computer and economic scientists; theoretical chemists and biologists, as well as all mathematically educated scientists and students, both in industry and academia, interested in predicting and controlling complex dynamical systems of arbitrary nature.

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