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Complex Nonlinearity
Vladimir G. Ivancevic, Tijana T. Ivancevic (Gebundene Ausgabe, Englisch)
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Beschreibung
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. The objective of this book is to provide a serious reader with a serious scientific tool that willenable 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
23.06.2008
Sprache
Englisch
EAN
9783540793564
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Understanding Complex Systems
Sonderedition
Nein
Autor
Vladimir G. Ivancevic, Tijana T. Ivancevic
Seitenanzahl
844
Einbandart
Gebundene Ausgabe
Buch Untertitel
Chaos, Phase Transitions, Topology Change and Path Integrals
Schlagwörter
Chaos, Complex Nonlinearity, Complexity, Nonlinear system, Nonlinearity, Path Integrals, Phase Transitions, Topology Change, complex system, complex systems, nonlinear dynamics
Thema-Inhalt
GPFC - Kybernetik und Systemtheorie
TGMD - Maschinenbau: Festkörpermechanik
TBJ - Mathematik für Ingenieure
PHU - Mathematische Physik
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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