Spinning Tops

A Course on Integrable Systems
Author: M. Audin
Publisher: Cambridge University Press
ISBN: 9780521779197
Category: Mathematics
Page: 148
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Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.

Integrable Systems in the Realm of Algebraic Geometry


Author: Pol Vanhaecke
Publisher: Springer Science & Business Media
ISBN: 3540423370
Category: Mathematics
Page: 264
View: 6426
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Integrable Systems, Topology, and Physics

A Conference on Integrable Systems in Differential Geometry, University of Tokyo, Japan, July 17-21, 2000
Author: Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Publisher: American Mathematical Soc.
ISBN: 0821829394
Category: Mathematics
Page: 324
View: 5184
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Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the second of three collections of expository and research articles. This volume focuses on topology and physics. The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it.Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations - all of these areas have gained from the integrable systems point of view and contributed to it. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The first volume from this conference, also available from the 'AMS', is ""Differential Geometry and Integrable Systems, Volume 308"" in the ""Contemporary Mathematics"" series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the 'AMS' in the ""Advanced Studies in Pure Mathematics"" series.

Algebraic Integrability, Painlevé Geometry and Lie Algebras


Author: Mark Adler,Pierre van Moerbeke,Pol Vanhaecke
Publisher: Springer Science & Business Media
ISBN: 366205650X
Category: Mathematics
Page: 484
View: 5213
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Handbook of Differential Geometry


Author: Franki J.E. Dillen,Leopold C.A. Verstraelen
Publisher: Elsevier
ISBN: 9780080461205
Category: Mathematics
Page: 574
View: 3296
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In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics

Journal of Physics A

Mathematical and general
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematical physics
Page: N.A
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Choice

Publication of the Association of College and Research Libraries, a Division of the American Library Association
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Publisher: N.A
ISBN: N.A
Category: Academic libraries
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Journal of Physics

Mathematical and general. A
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Publisher: N.A
ISBN: N.A
Category: Mathematical physics
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Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
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American Book Publishing Record


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Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
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Introduction to Classical Integrable Systems


Author: Olivier Babelon,Denis Bernard,Michel Talon
Publisher: Cambridge University Press
ISBN: 9780521822671
Category: Mathematics
Page: 602
View: 7796
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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.

Discrete Systems and Integrability


Author: J. Hietarinta,N. Joshi,F. W. Nijhoff
Publisher: Cambridge University Press
ISBN: 1316654087
Category: Mathematics
Page: N.A
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This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines.

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual
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Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
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Solitons

Differential Equations, Symmetries and Infinite Dimensional Algebras
Author: T. Miwa,M. Jimbo,E. Date
Publisher: Cambridge University Press
ISBN: 9780521561617
Category: Mathematics
Page: 108
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The goal of this book is to investigate the high degree of symmetry that lies hidden in integrable systems.

Introduction to the Statistical Physics of Integrable Many-body Systems


Author: Ladislav Šamaj,Zoltán Bajnok
Publisher: Cambridge University Press
ISBN: 1107067669
Category: Science
Page: N.A
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Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.

A First Course in General Relativity


Author: Bernard Schutz
Publisher: Cambridge University Press
ISBN: 0521887054
Category: Science
Page: 393
View: 1980
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Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.

Classical Mechanics

Transformations, Flows, Integrable and Chaotic Dynamics
Author: Joseph L. McCauley
Publisher: Cambridge University Press
ISBN: 9780521578820
Category: Science
Page: 469
View: 5435
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An advanced text for first-year graduate students in physics and engineering taking a standard classical mechanics course, this is the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability. It introduces flows in phase space and transformations early and illustrates their applications throughout the text. The standard integrable problems of elementary physics are analyzed from the standpoint of flows, transformations, and integrability. This approach allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

Introduction to Calculus and Analysis


Author: Richard Courant,Fritz John
Publisher: Springer Science & Business Media
ISBN: 9783540665694
Category: Mathematics
Page: 556
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Biography of Richard Courant Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence. For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John. (P.D. Lax) Biography of Fritz John Fritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was half-Jewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994. John's research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMO-functions (bounded mean oscillations). Fritz John's work exemplifies the unity of mathematics as well as its elegance and its beauty. (J. Moser)

Quantum Field Theory in Condensed Matter Physics


Author: Alexei M. Tsvelik
Publisher: Cambridge University Press
ISBN: 1139440500
Category: Science
Page: N.A
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This book is a course in modern quantum field theory as seen through the eyes of a theorist working in condensed matter physics. It contains a gentle introduction to the subject and therefore can be used even by graduate students. The introductory parts include a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals including a discussion of Landau–Fermi liquid theory. In later chapters the discussion gradually turns to more advanced methods used in the theory of strongly correlated systems. The book contains a thorough exposition of such non-perturbative techniques as 1/N-expansion, bosonization (Abelian and non-Abelian), conformal field theory and theory of integrable systems. The book is intended for graduate students, postdoctoral associates and independent researchers working in condensed matter physics.

Combinatorics and Random Matrix Theory


Author: Jinho Baik,Percy Deift,Toufic Suidan
Publisher: American Mathematical Soc.
ISBN: 0821848410
Category: Combinatorial analysis
Page: 461
View: 6774
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Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.