LEADER 05560nam 2200721 a 450 001 9910464496603321 005 20200520144314.0 010 $a1-283-23479-3 010 $a9786613234797 010 $a981-4327-16-6 035 $a(CKB)3400000000016738 035 $a(EBL)840559 035 $a(OCoLC)754792913 035 $a(SSID)ssj0000539589 035 $a(PQKBManifestationID)12216360 035 $a(PQKBTitleCode)TC0000539589 035 $a(PQKBWorkID)10581123 035 $a(PQKB)11787739 035 $a(MiAaPQ)EBC840559 035 $a(WSP)00007960 035 $a(Au-PeEL)EBL840559 035 $a(CaPaEBR)ebr10493515 035 $a(CaONFJC)MIL323479 035 $a(EXLCZ)993400000000016738 100 $a20100723d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear dynamical systems of mathematical physics$b[electronic resource] $espectral and symplectic integrability analysis /$fDenis Blackmore, Anatoliy K. Prykarpatsky, Valeriy Hr. Samoylenko 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$dc2011 215 $a1 online resource (563 p.) 300 $aDescription based upon print version of record. 311 $a981-4327-15-8 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; Chapter 1 General Properties of Nonlinear Dynamical Systems; 1.1 Finite-dimensional dynamical systems; 1.1.1 Invariant measure; 1.1.2 The Liouville condition; 1.1.3 The Poincare? theorem; 1.1.4 The Birkhoff-Khinchin theorem; 1.1.5 The Birkhoff-Khinchin theorem for discrete dynamical systems; 1.2 Poissonian and symplectic structures on manifolds; 1.2.1 Poisson brackets; 1.2.2 The Liouville theorem and Hamilton-Jacobi method; 1.2.3 Dirac reduction: Symplectic and Poissonian structures on submanifolds 327 $aChapter 2 Geometric and Algebraic Properties of Nonlinear Dynamical Systems with Symmetry: Theory and Applications2.1 The Poisson structures and Lie group actions on manifolds: Introduction; 2.2 Lie group actions on Poisson manifolds and the orbit structure; 2.3 The canonical reduction method on symplectic spaces and related geometric structures on principal fiber bundles; 2.4 The form of reduced symplectic structures on cotangent spaces to Lie group manifolds and associated canonical connections 327 $a2.5 The geometric structure of abelian Yang-Mills type gauge field equations via the reduction method2.6 The geometric structure of non-abelian Yang-Mills gauge field equations via the reduction method; 2.7 Classical and quantum integrability; 2.7.1 The quantization scheme, observables and Poisson manifolds; 2.7.2 The Hopf and quantum algebras; 2.7.3 Integrable flows related to Hopf algebras and their Poissonian representations; 2.7.4 Casimir elements and their special properties; 2.7.5 Poisson co-algebras and their realizations 327 $a2.7.6 Casimir elements and the Heisenberg-Weil algebra related structures2.7.7 The Heisenberg-Weil co-algebra structure and related integrable flows; Chapter 3 Integrability by Quadratures of Hamiltonian and Picard-Fuchs Equations: Modern Differential-Geometric Aspects; 3.1 Introduction; 3.2 Preliminaries; 3.3 Integral submanifold embedding problem for an abelian Lie algebra of invariants; 3.4 Integral submanifold embedding problem for a nonabelian Lie algebra of invariants; 3.5 Examples; 3.6 Existence problem for a global set of invariants; 3.7 Additional examples 327 $a3.7.1 The Henon-Heiles system3.7.2 A truncated four-dimensional Fokker-Planck Hamiltonian system; Chapter 4 Infinite-dimensional Dynamical Systems; 4.1 Preliminary remarks; 4.2 Implectic operators and dynamical systems; 4.3 Symmetry properties and recursion operators; 4.4 Ba?cklund transformations; 4.5 Properties of solutions of some infinite sequences of dynamical systems; 4.6 Integro-differential systems; Chapter 5 Integrability Criteria for Dynamical Systems: the Gradient-Holonomic Algorithm; 5.1 The Lax representation; 5.1.1 Generalized eigenvalue problem 327 $a5.1.2 Properties of the spectral problem 330 $aThis distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, 606 $aDifferentiable dynamical systems 606 $aNonlinear theories 606 $aSymplectic geometry 606 $aSpectrum analysis$xMathematics 608 $aElectronic books. 615 0$aDifferentiable dynamical systems. 615 0$aNonlinear theories. 615 0$aSymplectic geometry. 615 0$aSpectrum analysis$xMathematics. 676 $a530.15/539 700 $aBlackmore$b Denis L$0863325 701 $aPrikarpatskii?$b A. K$g(Anatolii? Karolevich)$0972017 701 $aSamoylenko$b Valeriy Hr$0972018 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464496603321 996 $aNonlinear dynamical systems of mathematical physics$92210066 997 $aUNINA LEADER 01120nam0 22003133i 450 001 UFI0355579 005 20231121125908.0 010 $a9004117954 100 $a20151016d2001 ||||0itac50 ba 101 | $aeng 102 $anl 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 1 $a˜The œchallenge of epic$eallusive engagement in the Dionysiaca of Nonnus$fby Robert Shorrock 210 $aLeiden [etc.]$cBrill$d2001 215 $aVIII, 245 p.$d25 cm 225 | $aMnemosyne. Supplementum$v210 300 $aBibliogr. P. [215]-227. 410 0$1001CFI0162368$12001 $aMnemosyne. Supplementum$v210 606 $aNonno : di Panopoli . 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