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Nonlinear dynamical systems of mathe...

Blackmore, Denis L.

Nonlinear dynamical systems of mathematical physicsspectral and symplectic integrability analysis /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlinear dynamical systems of mathematical physicsDenis Blackmore, Anatoliy K. Prykarpatsky, Valeriy Hr Samoylenko.
Reminder of title:	spectral and symplectic integrability analysis /
Author:	Blackmore, Denis L.
other author:	Prykarpats'kyi, A. K.
Published:	Singapore ;World Scientific Pub. Co.,c2011.
Description:	xix, 542 p.
Subject:	Differentiable dynamical systems.
Online resource:	http://www.worldscientific.com/worldscibooks/10.1142/7960#t=toc
ISBN:	9789814327169 (electronic bk.)

Nonlinear dynamical systems of mathematical physicsspectral and symplectic integrability analysis /
Blackmore, Denis L.

Nonlinear dynamical systems of mathematical physicsspectral and symplectic integrability analysis /[electronic resource] :Denis Blackmore, Anatoliy K. Prykarpatsky, Valeriy Hr Samoylenko. - Singapore ;World Scientific Pub. Co.,c2011. - xix, 542 p.

Includes bibliographical references (p. 517-538) and index.

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.

Electronic reproduction.
Singapore :
World Scientific Publishing Co.,
2011.

System requirements: Adobe Acrobat Reader.

ISBN: 9789814327169 (electronic bk.)Subjects--Topical Terms:

183764
Differentiable dynamical systems.

LC Class. No.: QA614.8

Dewey Class. No.: 530.15539

Nonlinear dynamical systems of mathematical physicsspectral and symplectic integrability analysis /
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300 $a xix, 542 p.
504 $a Includes bibliographical references (p. 517-538) and index.
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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