Integrable Systems Of Classical Mechanics And Lie Algebras Volume I PDF Download
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| Author | : PERELOMOV |
| Publisher | : Birkhäuser |
| Total Pages | : 312 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034892578 |
Download Integrable Systems of Classical Mechanics and Lie Algebras Volume I Book in PDF, ePub and Kindle
This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view. Chapter 5 investigates some additional topics related to many-body systems. The book will be valuable to students as well as researchers.
| Author | : PERELOMOV |
| Publisher | : Birkhäuser |
| Total Pages | : 308 |
| Release | : 2011-09-28 |
| Genre | : Science |
| ISBN | : 9783034892582 |
Download Integrable Systems of Classical Mechanics and Lie Algebras Book in PDF, ePub and Kindle
| Author | : Askolʹd Mikhaĭlovich Perelomov |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1990 |
| Genre | : Hamiltonian systems |
| ISBN | : 9780817623364 |
Download Integrable Systems of Classical Mechanics and Lie Algebras Book in PDF, ePub and Kindle
| Author | : A. M. Perelomov |
| Publisher | : Springer |
| Total Pages | : 328 |
| Release | : 1990 |
| Genre | : Electronic books |
| ISBN | : |
Download Integrable Systems of Classical Mechanics and Lie Algebras Book in PDF, ePub and Kindle
This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view. Chapter 5 investigates some additional topics related to many-body systems. The book will be valuable to students as well as researchers.
| Author | : Askolʹd Mikhaĭlovich Perelomov |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1990 |
| Genre | : Hamiltonian systems |
| ISBN | : |
Download Integrable Systems of Classical Mechanics and Lie Algebras Book in PDF, ePub and Kindle
| Author | : Askold M. Perelomov |
| Publisher | : |
| Total Pages | : |
| Release | : |
| Genre | : |
| ISBN | : |
Download Integrable Systems of Classical Mechanics and Lie Algebras Book in PDF, ePub and Kindle
| Author | : Olivier Babelon |
| Publisher | : Cambridge University Press |
| Total Pages | : 622 |
| Release | : 2003-04-17 |
| Genre | : Mathematics |
| ISBN | : 9780521822671 |
Download Introduction to Classical Integrable Systems Book in PDF, ePub and Kindle
This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.
| Author | : Matteo Petrera |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2015 |
| Genre | : Differential equations, Nonlinear |
| ISBN | : 9783832539504 |
Download Mathematical Physics III - Integrable Systems of Classical Mechanics Book in PDF, ePub and Kindle
These Lecture Notes provide an introduction to the modern theory of classical finite-dimensional integrable systems. The first chapter focuses on some classical topics of differential geometry. This should help the reader to get acquainted with the required language of smooth manifolds, Lie groups and Lie algebras. The second chapter is devoted to Poisson and symplectic geometry with special emphasis on the construction of finite-dimensional Hamiltonian systems. Multi-Hamiltonian systems are also considered. In the third chapter the classical theory of Arnold-Liouville integrability is presented, while chapter four is devoted to a general overview of the modern theory of integrability. Among the topics covered are: Lie-Poisson structures, Lax formalism, double Lie algebras, R-brackets, Adler-Kostant-Symes scheme, Lie bialgebras, r-brackets. Some examples (Toda system, Garnier system, Gaudin system, Lagrange top) are presented in chapter five. They provide a concrete illustration of the theoretical part. Finally, the last chapter is devoted to a short overview of the problem of integrable discretization.
| Author | : A. T. Fomenko |
| Publisher | : CRC Press |
| Total Pages | : 316 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : 9782881241703 |
Download Integrable Systems on Lie Algebras and Symmetric Spaces Book in PDF, ePub and Kindle
Second volume in the series, translated from the Russian, sets out new regular methods for realizing Hamilton's canonical equations in Lie algebras and symmetric spaces. Begins by constructing the algebraic embeddings in Lie algebras of Hamiltonian systems, going on to present effective methods for constructing complete sets of functions in involution on orbits of coadjoint representations of Lie groups. Ends with the proof of the full integrability of a wide range of many- parameter families of Hamiltonian systems that allow algebraicization. Annotation copyrighted by Book News, Inc., Portland, OR
| Author | : Richard H. Cushman |
| Publisher | : Birkhäuser |
| Total Pages | : 493 |
| Release | : 2015-06-01 |
| Genre | : Science |
| ISBN | : 3034809182 |
Download Global Aspects of Classical Integrable Systems Book in PDF, ePub and Kindle
This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.
