Nonlinear dynamical systems of mathematical physics: spectral and symplectic integrability analysis
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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World Scientific
c2011
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| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index 1. General properties of nonlinear dynamical systems. 1.1. Finite-dimensional dynamical systems. 1.2. Poissonian and symplectic structures on manifolds -- 2. Nonlinear dynamical systems with symmetry. 2.1. 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. 2.5. The geometric structure of abelian Yang-Mills type gauge field equations via the reduction method. 2.6. The geometric structure of non-abelian Yang-Mills gauge field equations via the reduction method. 2.7. Classical and quantum integrability -- - 3. Integrability by quadratures. 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 -- 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. Backlund transformations. 4.5. Properties of solutions of some infinite sequences of dynamical systems. 4.6. Integro-differential systems -- 5. Integrability : The gradient-holonomic algorithm. 5.1. The Lax representation. 5.2. Recursive operators and conserved quantities. 5.3. Existence criteria for a Lax representation. 5.4. The current Lie algebra on a cycle : A symmetry subalgebra of compatible bi-Hamiltonian nonlinear dynamical systems -- - 6. Algebraic, differential and geometric aspects of integrability. 6.1. A non-isospectrally Lax integrable KdV dynamical system. 6.2. Algebraic structure of the gradient-holonomic algorithm for Lax integrable systems This 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, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems |
| Beschreibung: | 1 Online-Ressource (xix, 542 p.) |
| ISBN: | 9789814327152 9789814327169 9814327158 9814327166 |
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| 500 | |a 1. General properties of nonlinear dynamical systems. 1.1. Finite-dimensional dynamical systems. 1.2. Poissonian and symplectic structures on manifolds -- 2. Nonlinear dynamical systems with symmetry. 2.1. 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. 2.5. The geometric structure of abelian Yang-Mills type gauge field equations via the reduction method. 2.6. The geometric structure of non-abelian Yang-Mills gauge field equations via the reduction method. 2.7. Classical and quantum integrability -- | ||
| 500 | |a - 3. Integrability by quadratures. 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 -- 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. Backlund transformations. 4.5. Properties of solutions of some infinite sequences of dynamical systems. 4.6. Integro-differential systems -- 5. Integrability : The gradient-holonomic algorithm. 5.1. The Lax representation. 5.2. Recursive operators and conserved quantities. 5.3. Existence criteria for a Lax representation. 5.4. The current Lie algebra on a cycle : A symmetry subalgebra of compatible bi-Hamiltonian nonlinear dynamical systems -- | ||
| 500 | |a - 6. Algebraic, differential and geometric aspects of integrability. 6.1. A non-isospectrally Lax integrable KdV dynamical system. 6.2. Algebraic structure of the gradient-holonomic algorithm for Lax integrable systems | ||
| 500 | |a This 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, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems | ||
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| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a Symplectic geometry | |
| 650 | 4 | |a Spectrum analysis |x Mathematics | |
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Datensatz im Suchindex
| _version_ | 1804175524963024896 |
|---|---|
| any_adam_object | |
| author | Blackmore, Denis L. |
| author_facet | Blackmore, Denis L. |
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| author_sort | Blackmore, Denis L. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/539 |
| dewey-search | 530.15/539 |
| dewey-sort | 3530.15 3539 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV043108183 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:40Z |
| institution | BVB |
| isbn | 9789814327152 9789814327169 9814327158 9814327166 |
| language | English |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xix, 542 p.) |
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| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | World Scientific |
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| spelling | Blackmore, Denis L. Verfasser aut Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis Denis Blackmore, Anatoliy K. Prykarpatsky, Valeriy Hr. Samoylenko Singapore World Scientific c2011 1 Online-Ressource (xix, 542 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index 1. General properties of nonlinear dynamical systems. 1.1. Finite-dimensional dynamical systems. 1.2. Poissonian and symplectic structures on manifolds -- 2. Nonlinear dynamical systems with symmetry. 2.1. 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. 2.5. The geometric structure of abelian Yang-Mills type gauge field equations via the reduction method. 2.6. The geometric structure of non-abelian Yang-Mills gauge field equations via the reduction method. 2.7. Classical and quantum integrability -- - 3. Integrability by quadratures. 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 -- 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. Backlund transformations. 4.5. Properties of solutions of some infinite sequences of dynamical systems. 4.6. Integro-differential systems -- 5. Integrability : The gradient-holonomic algorithm. 5.1. The Lax representation. 5.2. Recursive operators and conserved quantities. 5.3. Existence criteria for a Lax representation. 5.4. The current Lie algebra on a cycle : A symmetry subalgebra of compatible bi-Hamiltonian nonlinear dynamical systems -- - 6. Algebraic, differential and geometric aspects of integrability. 6.1. A non-isospectrally Lax integrable KdV dynamical system. 6.2. Algebraic structure of the gradient-holonomic algorithm for Lax integrable systems This 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, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Differentiable dynamical systems Nonlinear theories Symplectic geometry Spectrum analysis Mathematics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Globale Analysis (DE-588)4021285-3 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Globale Analysis (DE-588)4021285-3 s Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 Prikarpatskij, Anatolij K. Sonstige oth Samoylenko, Valeriy Hr. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389627 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Blackmore, Denis L. Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Differentiable dynamical systems Nonlinear theories Symplectic geometry Spectrum analysis Mathematics Mathematische Physik (DE-588)4037952-8 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Globale Analysis (DE-588)4021285-3 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4126142-2 (DE-588)4021285-3 |
| title | Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis |
| title_auth | Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis |
| title_exact_search | Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis |
| title_full | Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis Denis Blackmore, Anatoliy K. Prykarpatsky, Valeriy Hr. Samoylenko |
| title_fullStr | Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis Denis Blackmore, Anatoliy K. Prykarpatsky, Valeriy Hr. Samoylenko |
| title_full_unstemmed | Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis Denis Blackmore, Anatoliy K. Prykarpatsky, Valeriy Hr. Samoylenko |
| title_short | Nonlinear dynamical systems of mathematical physics |
| title_sort | nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis |
| title_sub | spectral and symplectic integrability analysis |
| topic | SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Differentiable dynamical systems Nonlinear theories Symplectic geometry Spectrum analysis Mathematics Mathematische Physik (DE-588)4037952-8 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Globale Analysis (DE-588)4021285-3 gnd |
| topic_facet | SCIENCE / Physics / Mathematical & Computational Mathematik Differentiable dynamical systems Nonlinear theories Symplectic geometry Spectrum analysis Mathematics Mathematische Physik Nichtlineares dynamisches System Globale Analysis |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389627 |
| work_keys_str_mv | AT blackmoredenisl nonlineardynamicalsystemsofmathematicalphysicsspectralandsymplecticintegrabilityanalysis AT prikarpatskijanatolijk nonlineardynamicalsystemsofmathematicalphysicsspectralandsymplecticintegrabilityanalysis AT samoylenkovaleriyhr nonlineardynamicalsystemsofmathematicalphysicsspectralandsymplecticintegrabilityanalysis |