Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds
DOWNLOAD
Download Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds
DOWNLOAD
Author : A.K. Prykarpatsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds written by A.K. Prykarpatsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.
In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).
Nonlinear Dynamical Systems Of Mathematical Physics
DOWNLOAD
Author :
language : en
Publisher:
Release Date :
Nonlinear Dynamical Systems Of Mathematical Physics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Nonlinear Dynamical Systems Of Mathematical Physics
DOWNLOAD
Author : Denis L. Blackmore
language : en
Publisher: World Scientific
Release Date : 2011
Nonlinear Dynamical Systems Of Mathematical Physics written by Denis L. Blackmore and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.
Integrability Of Nonlinear Systems
DOWNLOAD
Author : Yvette Kosmann-Schwarzbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-17
Integrability Of Nonlinear Systems written by Yvette Kosmann-Schwarzbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-17 with Science categories.
The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
Geometry And Dynamics Of Integrable Systems
DOWNLOAD
Author : Alexey Bolsinov
language : en
Publisher: Birkhäuser
Release Date : 2016-10-27
Geometry And Dynamics Of Integrable Systems written by Alexey Bolsinov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-27 with Mathematics categories.
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.
Group Theoretical Methods For Integration Of Nonlinear Dynamical Systems
DOWNLOAD
Author : A.N. Leznov
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-04-22
Group Theoretical Methods For Integration Of Nonlinear Dynamical Systems written by A.N. Leznov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-22 with Mathematics categories.
The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view.
Symmetries And Singularity Structures
DOWNLOAD
Author : Muthuswamy Lakshmanan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symmetries And Singularity Structures written by Muthuswamy Lakshmanan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Proceedings of the Workshop, Bharathidasan University, Tiruchirapalli, India, November 29 - December 2, 1989
Dynamical Systems Vii
DOWNLOAD
Author : V.I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14
Dynamical Systems Vii written by V.I. Arnol'd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-14 with Mathematics categories.
A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.
Discrete Integrable Systems
DOWNLOAD
Author : Basil Grammaticos
language : en
Publisher: Springer
Release Date : 2004-06-22
Discrete Integrable Systems written by Basil Grammaticos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-22 with Science categories.
This volume consists of a set of ten lectures conceived as both introduction and up-to-date survey on discrete integrable systems. It constitutes a companion book to "Integrability of Nonlinear Systems" (Springer-Verlag, 2004, LNP 638, ISBN 3-540-20630-2). Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
Averaging Methods In Nonlinear Dynamical Systems
DOWNLOAD
Author : Jan A. Sanders
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Averaging Methods In Nonlinear Dynamical Systems written by Jan A. Sanders and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.