Differential Geometry And Integrable Systems

Differential Geometry And Integrable Systems Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Differential Geometry And Integrable Systems book. This book definitely worth reading, it is an incredibly well-written.

Differential Geometry and Integrable Systems

Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Differential Geometry and Integrable Systems Book PDF

Author : Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Publisher : American Mathematical Soc.
Page : 349 pages
File Size : 45,7 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829387

Get Book

Differential Geometry and Integrable Systems by Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita Pdf

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 first of three collections of expository and research articles. This volume focuses on differential geometry. It is remarkable that many classical objects in surface theory and submanifold theory are described as integrable systems. Having such a description generally reveals previously unnoticed symmetries and can lead to surprisingly explicit solutions.Surfaces of constant curvature in Euclidean space, harmonic maps from surfaces to symmetric spaces, and analogous structures on higher-dimensional manifolds are some of the examples that have broadened the horizons of differential geometry, bringing a rich supply of concrete examples into the theory of integrable systems. 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 second volume from this conference, also available from the 'AMS', is ""Integrable Systems, Topology, and Physics, Volume 309"" 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.

Integrable Systems, Geometry, and Topology

Chuu-lian Terng
Integrable Systems Geometry and Topology Book PDF

Author : Chuu-lian Terng
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 52,5 Mb
Release : 2006
Category : Geometry
ISBN : 9780821840481

Get Book

Integrable Systems, Geometry, and Topology by Chuu-lian Terng Pdf

The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and theirrelations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu,and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of Yang-Mills-Higgs equations on Riemann surfaces. The article by Terng and Uhlenbeck explains the gauge equivalence of the matrix non-linear Schrödinger equation, the Schrödinger flow on Grassmanian, and the Heisenberg Feromagnetic model. The bookprovides an introduction to integrable systems and their relation to differential geometry. It is suitable for advanced graduate students and research mathematicians. Information for our distributors: Titles in this series are copublished with International Press, Cambridge, MA.

Geometry and Dynamics of Integrable Systems

Alexey Bolsinov,Juan J. Morales-Ruiz,Nguyen Tien Zung
Geometry and Dynamics of Integrable Systems Book PDF

Author : Alexey Bolsinov,Juan J. Morales-Ruiz,Nguyen Tien Zung
Publisher : Birkhäuser
Page : 140 pages
File Size : 47,8 Mb
Release : 2016-10-27
Category : Mathematics
ISBN : 9783319335032

Get Book

Geometry and Dynamics of Integrable Systems by Alexey Bolsinov,Juan J. Morales-Ruiz,Nguyen Tien Zung Pdf

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.

Discrete Differential Geometry

Alexander I. Bobenko,Yuri B. Suris
Discrete Differential Geometry Book PDF

Author : Alexander I. Bobenko,Yuri B. Suris
Publisher : American Mathematical Soc.
Page : 433 pages
File Size : 49,6 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821847008

Get Book

Discrete Differential Geometry by Alexander I. Bobenko,Yuri B. Suris Pdf

"An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of Integrable systems. One of the main goals of this book Is to reveal this integrable structure of discrete differential geometry." "The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question "How do we discretize differential geometry?" arising in their specific field."--BOOK JACKET.

Optimal Control and Geometry: Integrable Systems

Velimir Jurdjevic
Optimal Control and Geometry Integrable Systems Book PDF

Author : Velimir Jurdjevic
Publisher : Cambridge University Press
Page : 437 pages
File Size : 48,5 Mb
Release : 2016-07-04
Category : Mathematics
ISBN : 9781107113886

Get Book

Optimal Control and Geometry: Integrable Systems by Velimir Jurdjevic Pdf

Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics.

Integrable Systems, Topology, and Physics

Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Integrable Systems Topology and Physics Book PDF

Author : Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 45,9 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 9780821829394

Get Book

Integrable Systems, Topology, and Physics by Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita Pdf

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.

Integrable Systems and Algebraic Geometry

Ron Donagi,Tony Shaska
Integrable Systems and Algebraic Geometry Book PDF

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 537 pages
File Size : 48,9 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9781108715775

Get Book

Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Dynamical Systems VII

V.I. Arnol'd,S.P. Novikov
Dynamical Systems VII Book PDF

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 52,7 Mb
Release : 2013-12-14
Category : Mathematics
ISBN : 9783662067963

Get Book

Dynamical Systems VII by V.I. Arnol'd,S.P. Novikov Pdf

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.

Probability, Geometry and Integrable Systems

Mark Pinsky,Bjorn Birnir
Probability Geometry and Integrable Systems Book PDF

Author : Mark Pinsky,Bjorn Birnir
Publisher : Cambridge University Press
Page : 405 pages
File Size : 52,7 Mb
Release : 2008-03-17
Category : Mathematics
ISBN : 9780521895279

Get Book

Probability, Geometry and Integrable Systems by Mark Pinsky,Bjorn Birnir Pdf

Reflects the range of mathematical interests of Henry McKean, to whom it is dedicated.

Discrete Integrable Geometry and Physics

Alexander I. Bobenko,Ruedi Seiler
Discrete Integrable Geometry and Physics Book PDF

Author : Alexander I. Bobenko,Ruedi Seiler
Publisher : Clarendon Press
Page : 466 pages
File Size : 43,5 Mb
Release : 1999
Category : Mathematics
ISBN : 0198501609

Get Book

Discrete Integrable Geometry and Physics by Alexander I. Bobenko,Ruedi Seiler Pdf

Recent interactions between the fields of geometry, classical and quantum dynamical systems, and visualization of geometric objects such as curves and surfaces have led to the observation that most concepts of surface theory and of the theory of integrable systems have natural discreteanalogues. These are characterized by the property that the corresponding difference equations are integrable, and has led in turn to some important applications in areas of condensed matter physics and quantum field theory, amongst others. The book combines the efforts of a distinguished team ofauthors from various fields in mathematics and physics in an effort to provide an overview of the subject. The mathematical concepts of discrete geometry and discrete integrable systems are firstly presented as fundamental and valuable theories in themselves. In the following part these concepts areput into the context of classical and quantum dynamics.

Differential Geometry and Mathematical Physics

Gerd Rudolph,Matthias Schmidt
Differential Geometry and Mathematical Physics Book PDF

Author : Gerd Rudolph,Matthias Schmidt
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 50,8 Mb
Release : 2012-11-09
Category : Science
ISBN : 9789400753457

Get Book

Differential Geometry and Mathematical Physics by Gerd Rudolph,Matthias Schmidt Pdf

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Integrable Systems and Algebraic Geometry: Volume 1

Ron Donagi,Tony Shaska
Integrable Systems and Algebraic Geometry Volume 1 Book PDF

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 421 pages
File Size : 52,7 Mb
Release : 2020-04-02
Category : Mathematics
ISBN : 9781108803588

Get Book

Integrable Systems and Algebraic Geometry: Volume 1 by Ron Donagi,Tony Shaska Pdf

Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.

Lectures on Integrable Systems

Jens Hoppe
Lectures on Integrable Systems Book PDF

Author : Jens Hoppe
Publisher : Springer Science & Business Media
Page : 109 pages
File Size : 55,5 Mb
Release : 2008-09-15
Category : Science
ISBN : 9783540472742

Get Book

Lectures on Integrable Systems by Jens Hoppe Pdf

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.

Surveys on Geometry and Integrable Systems

Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Surveys on Geometry and Integrable Systems Book PDF

Author : Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Publisher : Advanced Studies in Pure Mathe
Page : 528 pages
File Size : 41,5 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015075648991

Get Book

Surveys on Geometry and Integrable Systems by Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita Pdf

The articles in this volume provide a panoramic view of the role of geometry in integrable systems, firmly rooted in surface theory but currently branching out in all directions.The longer articles by Bobenko (the Bonnet problem), Dorfmeister (the generalized Weierstrass representation), Joyce (special Lagrangian 3-folds) and Terng (geometry of soliton equations) are substantial surveys of several aspects of the subject. The shorter ones indicate more briefly how the classical ideas have spread throughout differential geometry, symplectic geometry, algebraic geometry, and theoretical physics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

Harmonic Maps, Loop Groups, and Integrable Systems

Martin A. Guest
Harmonic Maps Loop Groups and Integrable Systems Book PDF

Author : Martin A. Guest
Publisher : Cambridge University Press
Page : 202 pages
File Size : 50,5 Mb
Release : 1997-01-13
Category : Mathematics
ISBN : 0521589320

Get Book

Harmonic Maps, Loop Groups, and Integrable Systems by Martin A. Guest Pdf

University-level introduction that leads to topics of current research in the theory of harmonic maps.