Nonlinear dynamical systems of mathematical physics: spectral and symplectic integrability analysis
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 i...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2011
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| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | 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: | xix, 542 p |
| ISBN: | 9789814327169 |
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| 520 | |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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| discipline | Physik |
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| id | DE-604.BV044638273 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:53Z |
| institution | BVB |
| isbn | 9789814327169 |
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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 Pub. Co. c2011 xix, 542 p txt rdacontent c rdamedia cr rdacarrier 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 Differentiable dynamical systems Nonlinear theories Symplectic geometry Spectrum analysis / Mathematics Globale Analysis (DE-588)4021285-3 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 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 Prykarpats'kyi, A. K. Sonstige oth Samoylenko, Valeriy Hr Sonstige oth Erscheint auch als Druck-Ausgabe 9789814327152 (hbk.) Erscheint auch als Druck-Ausgabe 9814327158 (hbk.) http://www.worldscientific.com/worldscibooks/10.1142/7960#t=toc Verlag URL des Erstveroeffentlichers 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 Differentiable dynamical systems Nonlinear theories Symplectic geometry Spectrum analysis / Mathematics Globale Analysis (DE-588)4021285-3 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4021285-3 (DE-588)4126142-2 (DE-588)4037952-8 |
| 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 | Differentiable dynamical systems Nonlinear theories Symplectic geometry Spectrum analysis / Mathematics Globale Analysis (DE-588)4021285-3 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Differentiable dynamical systems Nonlinear theories Symplectic geometry Spectrum analysis / Mathematics Globale Analysis Nichtlineares dynamisches System Mathematische Physik |
| url | http://www.worldscientific.com/worldscibooks/10.1142/7960#t=toc |
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