Perturbation Theory in Periodic Problems for Two-Dimensional Integrable Systems PDF Download
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Author: I. M. Krichever
Publisher: CRC Press
ISBN: 9783718652181
Category : Mathematics
Languages : en
Pages : 118
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Book Description
Author: I. M. Krichever
Publisher: CRC Press
ISBN: 9783718652181
Category : Mathematics
Languages : en
Pages : 118
Get Book Here
Book Description
Author: Mark Pinsky
Publisher: Cambridge University Press
ISBN: 0521895278
Category : Mathematics
Languages : en
Pages : 405
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Book Description
Reflects the range of mathematical interests of Henry McKean, to whom it is dedicated.
Author: Sergej B. Kuksin
Publisher: Springer
ISBN: 3540479201
Category : Mathematics
Languages : en
Pages : 128
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Book Description
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.
Author: Giuseppe Gaeta
Publisher: Springer Nature
ISBN: 1071626213
Category : Science
Languages : en
Pages : 601
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Book Description
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.
Author: T. Voronov
Publisher: CRC Press
ISBN: 9783718651993
Category : Mathematics
Languages : en
Pages : 152
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Book Description
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.
Author: Victor M. Buchstaber
Publisher: Springer
ISBN: 3030048071
Category : Science
Languages : en
Pages : 226
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Book Description
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.
Author: Sergej B. Kuksin
Publisher: Clarendon Press
ISBN: 9780198503958
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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.
Author: Robert A. Meyers
Publisher: Springer Science & Business Media
ISBN: 1461418054
Category : Mathematics
Languages : en
Pages : 1885
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Book Description
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author: Angelo Vulpiani
Publisher: Springer Science & Business Media
ISBN: 9783540203070
Category : Science
Languages : en
Pages : 268
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Book Description
The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance.
Author: I. A. Kunin
Publisher: Springer Science & Business Media
ISBN: 3642817483
Category : Science
Languages : en
Pages : 301
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Book Description
Crystals and polycrystals,composites and polymers, grids and multibar systems can be considered as examples of media with microstructure. A characteristic feature of all such models is the existence of scale parameters which are connected with micro geometry or long-range interacting forces. As a result the corresponding theory must essentially be a nonlocal one. The book is devoted to a systematic investigation of effects of microstructure, inner degrees of freedom and nonlocality in elastic media. The propagation of linear and nonlinear waves in dispersive media, static problems, and the theory of defects are considered in detail. Much attention is paid to approximate models and limiting tran sitions to classical elasticity. The book can be considered as a revised and updated edition of the author's book under the same title published in Russian in 1975. The frrst volume presents a self-con tained theory of one-dimensional models. The theory of three-dimensional models will be considered in a forthcoming volume. The author would like to thank H. Lotsch and H. Zorsky who read the manuscript and offered many suggestions.
