LEADER 04607nam 2200685 450 001 9910146557603321 005 20210217194556.0 010 $a1-281-85505-7 010 $a9786611855055 010 $a3-540-79357-7 024 7 $a10.1007/978-3-540-79357-1 035 $a(CKB)1000000000492157 035 $a(EBL)371579 035 $a(OCoLC)272310708 035 $a(SSID)ssj0000292268 035 $a(PQKBManifestationID)11210929 035 $a(PQKBTitleCode)TC0000292268 035 $a(PQKBWorkID)10269172 035 $a(PQKB)11025868 035 $a(DE-He213)978-3-540-79357-1 035 $a(MiAaPQ)EBC371579 035 $a(MiAaPQ)EBC6352799 035 $a(PPN)127049304 035 $a(EXLCZ)991000000000492157 100 $a20210217d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComplex nonlinearity $echaos, phase transitions, topology change, and path integrals /$fVladimir G. Ivancevic, Tijana T. Ivancevic 205 $a1st ed. 2008. 210 1$aBerlin, Germany :$cSpringer,$d[2008] 210 4$dİ2008 215 $a1 online resource (857 p.) 225 1 $aUnderstanding complex systems 225 1 $aSpringer complexity 300 $aDescription based upon print version of record. 311 $a3-540-79356-9 320 $aIncludes bibliographical references (pages [713]-830) and index. 327 $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. 330 $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. 410 0$aUnderstanding complex systems. 410 0$aSpringer complexity. 606 $aDynamics 606 $aNonlinear control theory 606 $aNonlinear systems 615 0$aDynamics. 615 0$aNonlinear control theory. 615 0$aNonlinear systems. 676 $a629.836 700 $aIvancevic$b Vladimir G.$0965912 702 $aIvancevic$b Tijana T. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146557603321 996 $aComplex nonlinearity$92430770 997 $aUNINA