Bifurcation Theory, Mechanics and Physics, C.P. Bruter; A. Aragnol; A. Lichnorowicz

Автор: Kuznetsov Yuri A.
Название: Elements of Applied Bifurcation Theory
ISBN: 0387219064 ISBN-13(EAN): 9780387219066
Издательство: Springer
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Описание: Explains the basic phenomena of bifurcation theory. This book provides a student or researcher with the basis in nonlinear dynamical systems and their bifurcations, giving them the necessary understanding of the approaches, methods, results and terminology used in the modern applied mathematics literature.

Автор: Kielh?fer
Название: Bifurcation Theory
ISBN: 1461405017 ISBN-13(EAN): 9781461405016
Издательство: Springer
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Описание: In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.  

Автор: Guo, Shangjiang, Wu, Jianhong
Название: Bifurcation Theory of Functional Differential Equations
ISBN: 1461469910 ISBN-13(EAN): 9781461469919
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Описание: This book summarizes effective and general approaches and frameworks in the investigation of bifurcation phenomena for functional differential equations (FDEs). It provides all the tools from bifurcation theory and contains examples and applications.

Автор: Gerard Iooss; Daniel D. Joseph
Название: Elementary Stability and Bifurcation Theory
ISBN: 0387970681 ISBN-13(EAN): 9780387970684
Издательство: Springer
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Описание: In its most general form bifurcation theory is a theory of asymptotic solutions of nonlinear equations. By asymptotic solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. We have written this book for the broadest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, economists, and others whose work involves understanding asymptotic solutions of nonlinear differential equations. To accomplish our aims, we have thought it necessary to make the analysis: (1) general enough to apply to the huge variety of applications which arise in science and technology; and (2) simple enough so that it can be understood by persons whose mathe- matical training does not extend beyond the classical methods of analysis which were popular in the nineteenth century. Of course, it is not possible to achieve generality and simplicity in a perfect union but, in fact, the general theory is simpler than the detailed theory required for particular applications. The general theory abstracts from the detailed problems only the essential features and provides the student with the skeleton on which detailed structures of the applications must rest. lt is generally believed that the mathematical theory of bifurcation requires some functional analysis and some ofthe methods of topology and dynamics.

Автор: S.-N. Chow; J. K. Hale
Название: Methods of Bifurcation Theory
ISBN: 1461381614 ISBN-13(EAN): 9781461381617
Издательство: Springer
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Описание: An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied.

Автор: Golubitsky, Schaffer,
Название: Singularities and groups in bifurcation theory
ISBN: 0387966528 ISBN-13(EAN): 9780387966526
Издательство: Springer
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Описание: Preface.- Contents of Vol. I.- Introduction.- Group Theoretic Preliminaries.- Symmetry-Breaking in Steady-State Bifurcation.- Case Study 4: The Planar BГ©nard Problem.- Equivariant Normal Forms.- Equivariant Unfolding Theory.- Case Study 5: The Traction Problem for Mooney-Rivlin Material.- Symmetry-Breaking in Hopf Bifurcation.- Hopf Bifurcation with 0(2) Symmetry.- Further Examples of Hopf Bifurcation with Symmetry.- Mode Interactions.- Mode Interactions with 0(2) Symmetry.- Case Study 6: The Taylor-Couette System.- Bibliography.- Index.

Автор: Shangjiang Guo; Jianhong Wu
Название: Bifurcation Theory of Functional Differential Equations
ISBN: 1489988963 ISBN-13(EAN): 9781489988966
Издательство: Springer
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Описание: This book summarizes effective and general approaches and frameworks in the investigation of bifurcation phenomena for functional differential equations (FDEs). It provides all the tools from bifurcation theory and contains examples and applications.

Автор: Richard H. Rand; Dieter Armbruster
Название: Perturbation Methods, Bifurcation Theory and Computer Algebra
ISBN: 0387965890 ISBN-13(EAN): 9780387965895
Издательство: Springer
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Описание: Perturbation methods have always been an important tool for treating nonlinear differential equations. Methods covered include: Lindstedt`s method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction.

Автор: L. Salvadori
Название: Bifurcation Theory and Applications
ISBN: 3540129316 ISBN-13(EAN): 9783540129318
Издательство: Springer
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Автор: V. Gaiko
Название: Global Bifurcation Theory and Hilbert`s Sixteenth Problem
ISBN: 1461348196 ISBN-13(EAN): 9781461348191
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Описание: On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second Interna- tional Congress of Mathematicians in Paris. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154].

Автор: Martin Golubitsky; David G. Schaeffer
Название: Singularities and Groups in Bifurcation Theory
ISBN: 1461295335 ISBN-13(EAN): 9781461295334
Издательство: Springer
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Описание: This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob- lems and we hope to convert the reader to this view.

Автор: Hansj?rg Kielh?fer
Название: Bifurcation Theory
ISBN: 1493901400 ISBN-13(EAN): 9781493901401
Издательство: Springer
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Описание: This book examines the main theorems in bifurcation theory. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces and shows how to apply the theory.