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Complex nonlinearity : chaos, phase transitions, topology change, and path integrals

Author: Vladimir G Ivancevic; Tijana T Ivancevic
Publisher: Berlin : Springer, ©2008.
Series: Understanding complex systems.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change." "The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Vladimir G Ivancevic; Tijana T Ivancevic
ISBN: 9783540793564 3540793569 9783540793571 3540793577
OCLC Number: 225449456
Description: xv, 844 pages : illustrations ; 24 cm
Contents: Basics of nonlinear and chaotic dynamics --
Phase transitions and synergetics --
Geometry and toplogy change in complex systems --
Nonlinear dynamics of path integrals --
Complex nonlinearity : combining it all together.
Series Title: Understanding complex systems.
Responsibility: Vladimir G. Ivancevic, Tijana T. Ivancevic.
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Abstract:

This book provides serious readers with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive  Read more...

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From the reviews:"Intended as a graduate-level monographic textbook this volume is devoted to a topological-differential geometric approach to the four notions added in title: chaos, phase Read more...

 
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    schema:reviewBody ""Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change." "The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), 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 action-amplitude 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." "Complex Nonlinearity includes a comprehensive bibliography on the subject and a detailed Index. Target readership includes all researchers and students of complex nonlinear systems working both in industry/clinics and academia."--Jacket." ;
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