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Topological Classification of Integrable Systems

1991 Mathematics
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Release : 1991
Genre : Mathematics
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Book Synopsis Topological Classification of Integrable Systems by : A. T. Fomenko

Download or read book Topological Classification of Integrable Systems written by A. T. Fomenko. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, researchers have found new topological invariants of integrable Hamiltonian systems of differential equations and have constructed a theory for their topological classification. Each paper in this important collection describes one of the "building blocks" of the theory, and several of the works are devoted to applications to specific physical equation. In particular, this collection covers the new topological obstructions to integrability, a new Morse-type theory of Bott integrals, and classification of bifurcations of the Liouville tori in integral systems. The papers collected here grew out of the research seminar "Contemporary Geometrical Methods" at Moscow University, under the guidance of A T Fomenko, V V Trofimov, and A V Bolsinov. Bringing together contributions by some of the experts in this area, this collection is the first publication to treat this theory in a comprehensive way.

Integrable Hamiltonian Systems

2004-02-25 Mathematics
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Release : 2004-02-25
Genre : Mathematics
Kind : eBook
Book Rating : 429/5 ( reviews)

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Book Synopsis Integrable Hamiltonian Systems by : A.V. Bolsinov

Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov. This book was released on 2004-02-25. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

New Results in the Theory of Topological Classification of Integrable Systems

1995 Mathematics
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Release : 1995
Genre : Mathematics
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Book Rating : 803/5 ( reviews)

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Book Synopsis New Results in the Theory of Topological Classification of Integrable Systems by : A. T. Fomenko

Download or read book New Results in the Theory of Topological Classification of Integrable Systems written by A. T. Fomenko. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integrable Systems, Geometry, and Topology

2006 Mathematics
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Release : 2006
Genre : Mathematics
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Book Rating : 487/5 ( reviews)

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Book Synopsis Integrable Systems, Geometry, and Topology by : Chuu-lian Terng

Download or read book Integrable Systems, Geometry, and Topology written by Chuu-lian Terng. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integrable Systems, Topology, and Physics

2002 Mathematics
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Release : 2002
Genre : Mathematics
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Book Rating : 394/5 ( reviews)

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Book Synopsis Integrable Systems, Topology, and Physics by : Martin A. Guest

Download or read book Integrable Systems, Topology, and Physics written by Martin A. Guest. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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