A Memoir On Integrable Systems
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A Memoir On Integrable Systems
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Author : Yuri Fedorov
language : en
Publisher: Springer
Release Date : 2017-03-14
A Memoir On Integrable Systems written by Yuri Fedorov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-14 with Mathematics categories.
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
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Author : Yuri Fedorov
language : en
Publisher: Springer
Release Date : 2010-11-15
A Memoir On Integrable Systems written by Yuri Fedorov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-15 with Mathematics categories.
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 And Riemann Surfaces Of Infinite Genus
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Author : Martin Ulrich Schmidt
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Integrable Systems And Riemann Surfaces Of Infinite Genus written by Martin Ulrich Schmidt 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 1996 with Mathematics categories.
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.
Integrable Systems
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Author : Ahmed Lesfari
language : en
Publisher: John Wiley & Sons
Release Date : 2022-07-13
Integrable Systems written by Ahmed Lesfari and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-13 with Mathematics categories.
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
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Author : Decio Levi
language : en
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
Release Date : 2023-01-23
Continuous Symmetries And Integrability Of Discrete Equations written by Decio Levi and has been published by American Mathematical Society, Centre de Recherches Mathématiques this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-23 with Mathematics categories.
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
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Author : Ron Donagi
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-02
Integrable Systems And Algebraic Geometry written by Ron Donagi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-02 with Mathematics categories.
A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
Generic Hamiltonian Dynamical Systems Are Neither Integrable Nor Ergodic
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Author : Lawrence Markus
language : en
Publisher: American Mathematical Soc.
Release Date : 1974
Generic Hamiltonian Dynamical Systems Are Neither Integrable Nor Ergodic written by Lawrence Markus 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 1974 with Differential equations categories.
This memoir gives an introduction to Hamiltonian dynamical systems on symplectic manifolds, including definitions of Hamiltonian vector fields, Poisson brackets, integrals of motion, complete integrability, and ergodicity. A particularly complete treatment of action-angle coordinates is given. Historical background into the question of ergodicity and integrability in Hamiltonian systems is also given.
Topological Methods In The Theory Of Integrable Systems
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Author : Alekseĭ Viktorovich Bolsinov
language : en
Publisher:
Release Date : 2006
Topological Methods In The Theory Of Integrable Systems written by Alekseĭ Viktorovich Bolsinov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume comprises selected papers on the subject of the topology of integrable systems theory which studies their qualitative properties, singularities and topological invariants. The aim of this volume is to develop the classification theory for integrable systems with two degrees of freedom which would allow for distinguishing such systems up to two natural equivalence relations. The first one is the equivalence of the associated foliations into Liouville tori. The second is the usual orbital equivalence. Also, general methods of classification theory are applied to the classical integrable problems in rigid body dynamics. In addition, integrable geodesic flows on two-dimensional surfaces are analysed from the viewpoint of the topology of integrable systems.
Side Iii
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Author : Decio Levi
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-06-15
Side Iii written by Decio Levi 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 2000-06-15 with Mathematics categories.
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
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Author : Alexey Borisov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-12-03
Rigid Body Dynamics written by Alexey Borisov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-03 with Science categories.
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