
Title  Complex Nonlinearity : Chaos, Phase Transitions, Topology Change and Path Integrals 
Author(s)  Ivancevic, Vladimir G;Ivancevic, Tijana T 
Publication  Berlin, Heidelberg, Springer Berlin Heidelberg, 2008. 
Description  XV, 844 p. 125 illus : online resource 
Abstract Note  Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of highdimensional complex systems of various physical and nonphysical nature and their underpinning geometrotopological change. The book starts with a textbooklike expose on nonlinear dynamics, attractors and chaos, both temporal and spatiotemporal, including modern techniques of chaos???control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and nonequilibrium, oscillatory, fractal and noiseinduced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity ??? chaos ??? corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their actionamplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman???s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia 
ISBN,Price  9783540793571 
Keyword(s)  1. APPLIED MATHEMATICS
2. COMPLEX SYSTEMS
3. DYNAMICAL SYSTEMS
4. Dynamical Systems and Ergodic Theory
5. DYNAMICS
6. EBOOK
7. EBOOK  SPRINGER
8. ENGINEERING MATHEMATICS
9. ERGODIC THEORY
10. Mathematical and Computational Engineering
11. STATISTICAL PHYSICS
12. Statistical Physics and Dynamical Systems
13. VIBRATION
14. Vibration, Dynamical Systems, Control

Item Type  eBook 
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Call#  Status  Issued To  Return Due On  Physical Location 
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