| Description |
1 online resource (xix, 589 pages) |
| Series |
Series on stability, vibration and control of systems, Series A ; volume 20 |
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Series on stability, vibration, and control of systems. Series A ; volume 20.
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| Contents |
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 |
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2.2.2 3D Rotations: Spinors2.2.3 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 |
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2.4.4 Invariant Hamiltonian Dynamics on Kahler Manifolds2.5 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 |
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""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"" |
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""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"" |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Differentiable dynamical systems.
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Chaotic behavior in systems.
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System analysis
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Control theory.
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Computational complexity.
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Systems Analysis
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systems analysis.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Chaotic behavior in systems
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Computational complexity
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Control theory
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Differentiable dynamical systems
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System analysis
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| Form |
Electronic book
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| Author |
Reid, Darryn J., author.
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| ISBN |
9789814635875 |
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9814635871 |
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9781680158502 |
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1680158503 |
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