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Complex Nonlinearity - Chaos, Phase Transitions, Topology Change and Path Integrals (Paperback, Softcover reprint of the original 1st ed. 2008)
Loot Price: R5,873
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Complex Nonlinearity - Chaos, Phase Transitions, Topology Change and Path Integrals (Paperback, Softcover reprint of the original 1st ed. 2008)
Series: Understanding Complex Systems
Expected to ship within 10 - 15 working days
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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
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.
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