A Memoir On Integrable Systems

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A Memoir on Integrable Systems

Yuri Fedorov,Valerij Vasilievich Kozlov
A Memoir on Integrable Systems Book PDF

Author : Yuri Fedorov,Valerij Vasilievich Kozlov
Publisher : Springer
Page : 0 pages
File Size : 55,7 Mb
Release : 2017-03-14
Category : Mathematics
ISBN : 3540590005

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A Memoir on Integrable Systems by Yuri Fedorov,Valerij Vasilievich Kozlov Pdf

This book considers the larger class of systems which are not (at least a priori) Hamiltonian but possess tensor invariants, in particular, an invariant measure. Several integrability theorems related to the existence of tensor invariants are formulated, and the authors illustrate the geometrical background of some classical and new hierarchies of integrable systems and give their explicit solution in terms of theta-functions. Most of the results discussed have not been published before, making this book immensely useful both to specialists in analytical dynamics who are interested in integrable problems and those in algebraic geometry who are looking for applications.

A Memoir on Integrable Systems

Yuri Fedorov,Valerij Vasilievich Kozlov
A Memoir on Integrable Systems Book PDF

Author : Yuri Fedorov,Valerij Vasilievich Kozlov
Publisher : Springer
Page : 280 pages
File Size : 46,6 Mb
Release : 2010-11-15
Category : Mathematics
ISBN : 3540863516

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A Memoir on Integrable Systems by Yuri Fedorov,Valerij Vasilievich Kozlov Pdf

This book considers the larger class of systems which are not (at least a priori) Hamiltonian but possess tensor invariants, in particular, an invariant measure. Several integrability theorems related to the existence of tensor invariants are formulated, and the authors illustrate the geometrical background of some classical and new hierarchies of integrable systems and give their explicit solution in terms of theta-functions. Most of the results discussed have not been published before, making this book immensely useful both to specialists in analytical dynamics who are interested in integrable problems and those in algebraic geometry who are looking for applications.

Integrable Systems

Ahmed Lesfari
Integrable Systems Book PDF

Author : Ahmed Lesfari
Publisher : John Wiley & Sons
Page : 340 pages
File Size : 47,6 Mb
Release : 2022-07-13
Category : Mathematics
ISBN : 9781786308276

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Integrable Systems by Ahmed Lesfari Pdf

This book illustrates the powerful interplay between topological, algebraic and complex analytical methods, within the field of integrable systems, by addressing several theoretical and practical aspects. Contemporary integrability results, discovered in the last few decades, are used within different areas of mathematics and physics. Integrable Systems incorporates numerous concrete examples and exercises, and covers a wealth of essential material, using a concise yet instructive approach. This book is intended for a broad audience, ranging from mathematicians and physicists to students pursuing graduate, Masters or further degrees in mathematics and mathematical physics. It also serves as an excellent guide to more advanced and detailed reading in this fundamental area of both classical and contemporary mathematics.

Continuous Symmetries and Integrability of Discrete Equations

Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Continuous Symmetries and Integrability of Discrete Equations Book PDF

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 40,5 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.

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 : 421 pages
File Size : 40,6 Mb
Release : 2020-04-02
Category : Mathematics
ISBN : 9781108715744

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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.

Integrable Systems and Riemann Surfaces of Infinite Genus

Martin Ulrich Schmidt
Integrable Systems and Riemann Surfaces of Infinite Genus Book PDF

Author : Martin Ulrich Schmidt
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 48,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804605

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Integrable Systems and Riemann Surfaces of Infinite Genus by Martin Ulrich Schmidt Pdf

This memoir develops the spectral theory of the Lax operators of nonlinear Schrodinger-like partial differential equations with periodic boundary conditions. Their spectral curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite genus. The points corresponding to infinite energy are added. The resulting spaces are no longer Riemann surfaces in the usual sense, but they are quite similar to compact Riemann surfaces. In fact, some of the basic tools of the theory of compact Riemann surfaces are generalized to these spectral curves and illuminate the structure of complete integrability: The eigen bundles define holomorphic line bundles on the spectral curves, which completely determine the potentials. These line bundles may be described by divisors of the same degree as the genus, and these divisors give rise to Darboux coordinates. With the help of a Riemann-Roch Theorem, the isospectral sets (the sets of all potentials corresponding to the same spectral curve) may be identified with open dense subsets of the Jacobian varieties. The real parts of the isospectral sets are infinite dimensional tori, and the group action solves the corresponding nonlinear partial differential equations. Deformations of the spectral curves are in one to one correspondence with holomorphic forms. Serre Duality reproduces the symplectic form.

Global Aspects of Classical Integrable Systems

Richard H. Cushman,Larry M. Bates
Global Aspects of Classical Integrable Systems Book PDF

Author : Richard H. Cushman,Larry M. Bates
Publisher : Birkhäuser
Page : 477 pages
File Size : 43,9 Mb
Release : 2015-06-01
Category : Science
ISBN : 9783034809184

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Global Aspects of Classical Integrable Systems by Richard H. Cushman,Larry M. Bates Pdf

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.

SIDE III

Decio Levi,Orlando Ragnisco
SIDE III Book PDF

Author : Decio Levi,Orlando Ragnisco
Publisher : American Mathematical Soc.
Page : 468 pages
File Size : 47,6 Mb
Release : 2000-06-15
Category : Mathematics
ISBN : 0821870211

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SIDE III by Decio Levi,Orlando Ragnisco Pdf

This volume contains the proceedings of the third meeting on ``Symmetries and Integrability of Difference Equations'' (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations--often referred to more generally as discrete systems--has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lie-type symmetries of differential-difference and difference-difference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete Painleve equations, difference and q-difference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discrete-time dynamical systems. The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.

Rigid Body Dynamics

Alexey Borisov,Ivan S. Mamaev
Rigid Body Dynamics Book PDF

Author : Alexey Borisov,Ivan S. Mamaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 533 pages
File Size : 53,5 Mb
Release : 2018-12-03
Category : Science
ISBN : 9783110544442

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Rigid Body Dynamics by Alexey Borisov,Ivan S. Mamaev Pdf

This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler – Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids

Lie Groups and Lie Algebras

B.P. Komrakov,I.S. Krasil'shchik,G.L. Litvinov,A.B. Sossinsky
Lie Groups and Lie Algebras Book PDF

Author : B.P. Komrakov,I.S. Krasil'shchik,G.L. Litvinov,A.B. Sossinsky
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401152587

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Lie Groups and Lie Algebras by B.P. Komrakov,I.S. Krasil'shchik,G.L. Litvinov,A.B. Sossinsky Pdf

This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.

On Some Aspects of the Theory of Anosov Systems

Grigorii A. Margulis
On Some Aspects of the Theory of Anosov Systems Book PDF

Author : Grigorii A. Margulis
Publisher : Springer Science & Business Media
Page : 144 pages
File Size : 55,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662090701

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On Some Aspects of the Theory of Anosov Systems by Grigorii A. Margulis Pdf

The seminal 1970 Moscow thesis of Grigoriy A. Margulis, published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing.

Infinite Dimensional Algebras and Quantum Integrable Systems

Petr P. Kulish,Nenad Manojlovic,Henning Samtleben
Infinite Dimensional Algebras and Quantum Integrable Systems Book PDF

Author : Petr P. Kulish,Nenad Manojlovic,Henning Samtleben
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 49,7 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373412

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Infinite Dimensional Algebras and Quantum Integrable Systems by Petr P. Kulish,Nenad Manojlovic,Henning Samtleben Pdf

This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.

New Trends in Quantum Integrable Systems

Boris Feigin,Michio Jimbo,Masato Okado
New Trends in Quantum Integrable Systems Book PDF

Author : Boris Feigin,Michio Jimbo,Masato Okado
Publisher : World Scientific
Page : 517 pages
File Size : 49,6 Mb
Release : 2010-10-29
Category : Mathematics
ISBN : 9789814324366

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New Trends in Quantum Integrable Systems by Boris Feigin,Michio Jimbo,Masato Okado Pdf

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

Integrability, Quantization, and Geometry: I. Integrable Systems

Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Integrability Quantization and Geometry I Integrable Systems Book PDF

Author : Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Publisher : American Mathematical Soc.
Page : 516 pages
File Size : 50,9 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455910

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Integrability, Quantization, and Geometry: I. Integrable Systems by Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman Pdf

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.

Class Field Theory

Georges Gras
Class Field Theory Book PDF

Author : Georges Gras
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 42,6 Mb
Release : 2005-02-16
Category : Mathematics
ISBN : 9783540441335

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Class Field Theory by Georges Gras Pdf

Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.