Perturbation Theory In Periodic Problems For Two Dimensional Integrable Systems
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Perturbation Theory In Periodic Problems For Two Dimensional Integrable Systems
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Author : I. M. Krichever
language : en
Publisher: CRC Press
Release Date : 1992
Perturbation Theory In Periodic Problems For Two Dimensional Integrable Systems written by I. M. Krichever and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Nearly Integrable Infinite Dimensional Hamiltonian Systems
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Author : Sergej B. Kuksin
language : en
Publisher: Springer
Release Date : 2006-11-15
Nearly Integrable Infinite Dimensional Hamiltonian Systems written by Sergej B. Kuksin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.
Recent Developments In Integrable Systems And Related Topics Of Mathematical Physics
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Author : Victor M. Buchstaber
language : en
Publisher: Springer
Release Date : 2018-12-30
Recent Developments In Integrable Systems And Related Topics Of Mathematical Physics written by Victor M. Buchstaber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-30 with Science categories.
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.
Geometric Integration Theory On Supermanifolds
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Author : T. Voronov
language : en
Publisher: CRC Press
Release Date : 1991
Geometric Integration Theory On Supermanifolds written by T. Voronov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
The author presents the first detailed and original account of his theory of forms on supermanifolds-a correct and non-trivial analogue of Cartan-de Rham theory based on new concepts. The paper develops the apparatus of supermanifold differential topology necessary for the integration theory. A key feature is the identification of a class of proper morphisms intimately connected with Berezin integration, which are of fundamental importance in various problems. The work also contains a condensed introduction to superanalysis and supermanifolds, free from algebraic formalism, which sets out afresh such challenging problems as the Berezin intgegral on a bounded domain.
Analysis Of Hamiltonian Pdes
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Author : Sergej B. Kuksin
language : en
Publisher: Clarendon Press
Release Date : 2000
Analysis Of Hamiltonian Pdes written by Sergej B. Kuksin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
For the last 20-30 years, interest among mathematicians and physicists in infinite-dimensional Hamiltonian systems and Hamiltonian partial differential equations has been growing strongly, and many papers and a number of books have been written on integrable Hamiltonian PDEs. During the last decade though, the interest has shifted steadily towards non-integrable Hamiltonian PDEs. Here, not algebra but analysis and symplectic geometry are the appropriate analysing tools. The present book is the first one to use this approach to Hamiltonian PDEs and present a complete proof of the "KAM for PDEs" theorem. It will be an invaluable source of information for postgraduate mathematics and physics students and researchers.
Probability Geometry And Integrable Systems
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Author : Mark Pinsky
language : en
Publisher: Cambridge University Press
Release Date : 2008-03-17
Probability Geometry And Integrable Systems written by Mark Pinsky 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 2008-03-17 with Mathematics categories.
Reflects the range of mathematical interests of Henry McKean, to whom it is dedicated.
First European Congress Of Mathematics Paris July 6 10 1992
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Author : Anthony Joseph
language : en
Publisher: Nelson Thornes
Release Date : 1994-07
First European Congress Of Mathematics Paris July 6 10 1992 written by Anthony Joseph and has been published by Nelson Thornes this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07 with Mathematics categories.
Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio Choice • J. Fröhlich: Mathematical Aspects of the Quantum Hall Effect • M. Giaquinta: Analytic and Geometric Aspects of Variational Problems for Vector Valued Mappings • U. Hamenstädt: Harmonic Measures for Leafwise Elliptic Operators Along Foliations • M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology • S.B. Kuksin: KAM-Theory for Partial Differential Equations • M. Laczkovich: Paradoxical Decompositions: A Survey of Recent Results • J.-F. Le Gall: A Path-Valued Markov Process and its Connections with Partial Differential Equations • I. Madsen: The Cyclotomic Trace in Algebraic K-Theory • A.S. Merkurjev: Algebraic K-Theory and Galois Cohomology • J. Nekovár: Values of L-Functions and p-Adic Cohomology • Y.A. Neretin: Mantles, Trains and Representations of Infinite Dimensional Groups • M.A. Nowak: The Evolutionary Dynamics of HIV Infections • R. Piene: On the Enumeration of Algebraic Curves - from Circles to Instantons • A. Quarteroni: Mathematical Aspects of Domain Decomposition Methods • A. Schrijver: Paths in Graphs and Curves on Surfaces • B. Silverman: Function Estimation and Functional Data Analysis • V. Strassen: Algebra and Complexity • P. Tukia: Generalizations of Fuchsian and Kleinian Groups • C. Viterbo: Properties of Embedded Lagrange Manifolds • D. Voiculescu: Alternative Entropies in Operator Algebras • M. Wodzicki : Algebraic K-Theory and Functional Analysis • D. Zagier: Values of Zeta Functions and Their Applications
Symmetry And Perturbation Theory
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Author : Giuseppe Gaeta
language : en
Publisher: World Scientific
Release Date : 2008
Symmetry And Perturbation Theory written by Giuseppe Gaeta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This proceedings volume is devoted to the interplay of symmetry and perturbation theory, as well as to cognate fields such as integrable systems, normal forms, n-body dynamics and choreographies, geometry and symmetry of differential equations, and finite and infinite dimensional dynamical systems. The papers collected here provide an up-to-date overview of the research in the field, and have many leading scientists in the field among their authors, including: D Alekseevsky, S Benenti, H Broer, A Degasperis, M E Fels, T Gramchev, H Hanssmann, J Krashil''shchik, B Kruglikov, D Krupka, O Krupkova, S Lombardo, P Morando, O Morozov, N N Nekhoroshev, F Oliveri, P J Olver, J A Sanders, M A Teixeira, S Terracini, F Verhulst, P Winternitz, B Zhilinskii. Sample Chapter(s). Foreword (101 KB). Chapter 1: Homogeneous Bi-Lagrangian Manifolds and Invariant Monge-Ampere Equations (415 KB). Contents: On Darboux Integrability (I M Anderson et al.); Computing Curvature without Christoffel Symbols (S Benenti); Natural Variational Principles (D Krupka); Fuzzy Fractional Monodromy (N N Nekhoroshev); Emergence of Slow Manifolds in Nonlinear Wave Equations (F Verhulst); Complete Symmetry Groups and Lie Remarkability (K Andriopoulos); Geodesically Equivalent Flat Bi-Cofactor Systems (K Marciniak); On the Dihedral N-Body Problem (A Portaluri); Towards Global Classifications: A Diophantine Approach (P van der Kamp); and other papers. Readership: Researchers and students (graduate/advanced undergraduates) in mathematics, applied mathematics, physics and nonlinear science.
Important Developments In Soliton Theory
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Author : A.S. Fokas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Important Developments In Soliton Theory written by A.S. Fokas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.
Perturbation Theory
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Author : Giuseppe Gaeta
language : en
Publisher: Springer Nature
Release Date : 2022-12-16
Perturbation Theory written by Giuseppe Gaeta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-16 with Science categories.
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.