000 04547nam a22005655i 4500
001 978-3-540-79357-1
003 DE-He213
005 20161121231053.0
007 cr nn 008mamaa
008 100301s2008 gw | s |||| 0|eng d
020 _a9783540793571
_9978-3-540-79357-1
024 7 _a10.1007/978-3-540-79357-1
_2doi
050 4 _aQC174.7-175.36
072 7 _aPHS
_2bicssc
072 7 _aPHDT
_2bicssc
072 7 _aSCI055000
_2bisacsh
082 0 4 _a621
_223
100 1 _aIvancevic, Vladimir G.
_eauthor.
245 1 0 _aComplex Nonlinearity
_h[electronic resource] :
_bChaos, Phase Transitions, Topology Change and Path Integrals /
_cby Vladimir G. Ivancevic, Tijana T. Ivancevic.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2008.
300 _aXV, 844 p. 125 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUnderstanding Complex Systems,
_x1860-0832
505 0 _aBasics of Nonlinear and Chaotic Dynamics -- Phase Transitions and Synergetics -- Geometry and Topology Change in Complex Systems -- Nonlinear Dynamics of Path Integrals -- Complex Nonlinearity: Combining It All Together.
520 _aComplex 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.
650 0 _aPhysics.
650 0 _aDynamics.
650 0 _aErgodic theory.
650 0 _aStatistical physics.
650 0 _aDynamical systems.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 0 _aVibration.
650 1 4 _aPhysics.
650 2 4 _aStatistical Physics, Dynamical Systems and Complexity.
650 2 4 _aVibration, Dynamical Systems, Control.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
700 1 _aIvancevic, Tijana T.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540793564
830 0 _aUnderstanding Complex Systems,
_x1860-0832
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-540-79357-1
912 _aZDB-2-PHA
950 _aPhysics and Astronomy (Springer-11651)
999 _c508114
_d508114