Integrable Systems in the realm of Algebraic Geometry

Integrable Systems in the realm of Algebraic Geometry

Author: Pol Vanhaecke

Publisher: Springer

Published: 2013-11-11

Total Pages: 226

ISBN-13: 3662215357

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Integrable systems are related to algebraic geometry in many different ways. This book deals with some aspects of this relation, the main focus being on the algebraic geometry of the level manifolds of integrable systems and the construction of integrable systems, starting from algebraic geometric data. For a rigorous account of these matters, integrable systems are defined on affine algebraic varieties rather than on smooth manifolds. The exposition is self-contained and is accessible at the graduate level; in particular, prior knowledge of integrable systems is not assumed.


Integrable Systems and Algebraic Geometry

Integrable Systems and Algebraic Geometry

Author: Ron Donagi

Publisher: Cambridge University Press

Published: 2020-04-02

Total Pages: 421

ISBN-13: 1108715745

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


Tropical Geometry and Integrable Systems

Tropical Geometry and Integrable Systems

Author: Chris Athorne

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 170

ISBN-13: 0821875531

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This volume contains the proceedings of the conference on tropical geometry and integrable systems, held July 3-8, 2011, at the University of Glasgow, United Kingdom. One of the aims of this conference was to bring together researchers in the field of tropical geometry and its applications, from apparently disparate ends of the spectrum, to foster a mutual understanding and establish a common language which will encourage further developments of the area. This aim is reflected in these articles, which cover areas from automata, through cluster algebras, to enumerative geometry. In addition, two survey articles are included which introduce ideas from researchers on one end of this spectrum to researchers on the other. This book is intended for graduate students and researchers interested in tropical geometry and integrable systems and the developing links between these two areas.


Algebraic Integrability, Painlevé Geometry and Lie Algebras

Algebraic Integrability, Painlevé Geometry and Lie Algebras

Author: Mark Adler

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 487

ISBN-13: 366205650X

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This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.


Integrable Systems and Foliations

Integrable Systems and Foliations

Author: Claude Albert

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 219

ISBN-13: 1461241340

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The articles in this volume are an outgrowth of a colloquium "Systemes Integrables et Feuilletages," which was held in honor of the sixtieth birthday of Pierre Molino. The topics cover the broad range of mathematical areas which were of keen interest to Molino, namely, integral systems and more generally symplectic geometry and Poisson structures, foliations and Lie transverse structures, transitive structures, and classification problems.


Recent Developments in Integrable Systems and Related Topics of Mathematical Physics

Recent Developments in Integrable Systems and Related Topics of Mathematical Physics

Author: Victor M. Buchstaber

Publisher: Springer

Published: 2018-12-30

Total Pages: 226

ISBN-13: 3030048071

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This volume, whose contributors include leading researchers in their field, covers a wide range of topics surrounding Integrable Systems, from theoretical developments to applications. Comprising a unique collection of research articles and surveys, the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.


Classical and Quantum Nonlinear Integrable Systems

Classical and Quantum Nonlinear Integrable Systems

Author: A Kundu

Publisher: CRC Press

Published: 2019-04-23

Total Pages: 320

ISBN-13: 9781420034615

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Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories


Geometric, Control and Numerical Aspects of Nonholonomic Systems

Geometric, Control and Numerical Aspects of Nonholonomic Systems

Author: Jorge Cortés Monforte

Publisher: Springer

Published: 2004-10-19

Total Pages: 235

ISBN-13: 3540457305

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Nonholonomic systems are a widespread topic in several scientific and commercial domains, including robotics, locomotion and space exploration. This work sheds new light on this interdisciplinary character through the investigation of a variety of aspects coming from several disciplines. The main aim is to illustrate the idea that a better understanding of the geometric structures of mechanical systems unveils new and unknown aspects to them, and helps both analysis and design to solve standing problems and identify new challenges. In this way, separate areas of research such as Classical Mechanics, Differential Geometry, Numerical Analysis or Control Theory are brought together in this study of nonholonomic systems.


Symmetry and Perturbation Theory

Symmetry and Perturbation Theory

Author: Simonetta Abenda

Publisher: World Scientific

Published: 2002

Total Pages: 306

ISBN-13: 9812382410

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Contents: An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and Schrodinger Equations (S Benenti); Partial Symmetries and Symmetric Sets of Solutions to PDEs (G Cicogna); Bifurcations in Flow-Induced Vibrations (S Fatimah & F Verhulst); Steklov-Lyapunov Type Systems (Y Fedorov); Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile); On the Linearization of holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev); On the Algebro Geometric Solution of a 3x3 Matrix Riemann-Hilbert Problem (v Enolskii & T Grava); Smooth Normalization of a Vector Field Near an Invariant Manifold ((a Kopanskii); Inverse Problems for SL(2) Lattices (V Kuznetsov); Some Remarks about the Geometry of Hamiltonian Conservation Laws (J P Ortega); Janet's Algorithm (W Plesken); Some Integrable Billiards (E Previato); Symmetries of Relative Equilibria for Simple Mechanical Systems (M R Olmos & M E S Dias); A Spectral Sequences Approach to Normal Forms (J Sanders); Rational Parametrization of Strata in Orbit Spaces of Compact Linear Groups (G Sartori & G Valente); Effective Hamiltonians and Perturbation Theory for Quantum Bound States of Nucleur Motion in Molecules (V Tyuterev); Generalized Hasimoto Transformation and Vector Sine-Gordon Equation (J P Wang); and other papers. Readership: Researchers and graduate students in mathematical and theoretical physics, and nonlinears science.