Integrable Systems Topology And Physics
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Integrable Systems Topology And Physics
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Author : Martin A. Guest
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Integrable Systems Topology And Physics written by Martin A. Guest and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Geometry, Differential categories.
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 CONM/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.
Lectures On Integrable Systems
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Author : Jens Hoppe
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-15
Lectures On Integrable Systems written by Jens Hoppe 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 2008-09-15 with Science categories.
Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.
Integrable Systems Quantum Groups And Quantum Field Theories
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Author : Alberto Ibort
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Systems Quantum Groups And Quantum Field Theories written by Alberto Ibort 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 Science categories.
In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.
Topology Geometry Integrable Systems And Mathematical Physics
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Author : V. M. Buchstaber
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-11-18
Topology Geometry Integrable Systems And Mathematical Physics written by V. M. Buchstaber and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-18 with Mathematics categories.
Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
Integrability Quantization And Geometry I Integrable Systems
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Author : Sergey Novikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-12
Integrability Quantization And Geometry I Integrable Systems written by Sergey Novikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-12 with Education categories.
This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Topology Geometry Integrable Systems And Mathematical Physics
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Author : Sergeĭ Petrovic Novikov
language : en
Publisher:
Release Date : 2014
Topology Geometry Integrable Systems And Mathematical Physics written by Sergeĭ Petrovic Novikov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Electronic books categories.
Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
Dynamical Systems Vii
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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.
Integrable Systems From Classical To Quantum
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Author : John P. Harnad
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Integrable Systems From Classical To Quantum written by John P. Harnad and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in r s3risingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.
New Results In The Theory Of Topological Classification Of Integrable Systems
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Author : A. T. Fomenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
New Results In The Theory Of Topological Classification Of Integrable Systems written by A. T. Fomenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This collection contains new results in the topological classification of integrable Hamiltonian systems. Recently, this subject has been applied to interesting problems in geometry and topology, classical mechanics, mathematical physics, and computer geometry. This new stage of development of the theory is reflected in this collection. Among the topics covered are: classification of some types of singularities of the moment map (including non-Bott types), computation of topological invariants for integrable systems describing various problems in mechanics and mathematical physics, construction of a theory of bordisms of integrable systems, and solution of some problems of symplectic topology arising naturally within this theory. A list of unsolved problems allows young mathematicians to become quickly involved in this active area of research.
Global Aspects Of Classical Integrable Systems
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Author : Richard H. Cushman
language : en
Publisher: Birkhäuser
Release Date : 2015-06-01
Global Aspects Of Classical Integrable Systems written by Richard H. Cushman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-01 with Science categories.
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.