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Sunday, October 4, 2020 | History

6 edition of Topics in stability and bifurcation theory. found in the catalog.

Topics in stability and bifurcation theory.

by David H. Sattinger

  • 11 Want to read
  • 17 Currently reading

Published by Springer-Verlag in Berlin .
Written in English


Edition Notes

SeriesLecture notes in mathematics -- 309
ID Numbers
Open LibraryOL15273596M
ISBN 103540061339

Structural stability and generic properties in Rn 4. Stability and bifurcation at a zero eigenvalue 5. Stability and bifurcation from a focus 6. First order bifurcation in the plane 7. Two dimensional periodic systems 8. Higher order bifurcation near equilibrium 9. A framework for infinite dimensions Bifurcation in infinite dimensions. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz global bifurcation theorem. Stability of the branches is.

Paperback / softback. Condition: New. New copy - Usually dispatched within 4 working days. Presents the general theory of first order bifurcation that occur for vector fields in finite dimensional space. This book includes formulation of structural stability and bifurcation in infinite dimensions. Seller Inventory # B Additional Physical Format: Online version: Iooss, Gérard. Elementary stability and bifurcation theory. New York: Springer-Verlag, © (OCoLC)

1. Introduction 2. On the definition of bifurcation 3. Structural stability and generic properties in $\mathbb {R}^n$ 4. Stability and bifurcation at a zero eigenvalue 5. Stability and bifurcation from a focus 6. First order bifurcation in the plane 7. Two dimensional periodic systems 8. Higher order bifurcation near equilibrium 9. The favorable reaction to the first edition of this book confirmed that the publication of such an application-oriented text on bifurcation theory of dynamical systems was well timed. The selected topics indeed cover ma-jor practical issues of applying the bifurcation theory .


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Topics in stability and bifurcation theory by David H. Sattinger Download PDF EPUB FB2

Topics in stability and bifurcation theory (Lecture notes in mathematics, ) Paperback – January 1, by David H Sattinger (Author) › Visit Amazon's David H Sattinger Page. Find all the books, read about the author, and more.

See search results for this author. Are you an author. Price: $ : Topics in Stability and Bifurcation Theory (Lecture Notes in Mathematics) (): Sattinger, David H.: BooksCited by: Topics in Stability and Bifurcation Theory. Authors; David H.

Sattinger; Book. Citations; k Downloads; Part of the Lecture Notes in Mathematics book series (LNM, volume ) Log in to check access. Buy eBook. USD Instant download; Readable on all devices; Own it forever; Local sales tax included if applicable.

Thus, bifurcation is a phenomenon closely related to the loss of stability in nonlinoar physical subjects of bifurcation and stability have always attracted the interest of pure mathematicians, beginning at least with Poincare and Lyapounov.

Book Title Topics in Stability and Bifurcation Theory Authors. David H. Sattinger; Series Title Lecture Notes in Mathematics Series Volume Copyright Publisher Springer-Verlag Berlin Heidelberg Copyright Holder Springer-Verlag Berlin Heidelberg eBook ISBN DOI /BFb Softcover ISBN Series ISSN Edition Number.

Overall, the book is a good source of information that should be consulted by anyone interested in bifurcation theory. The book contains material (like the bifurcation of forced T-periodic solutions) not normally included in an elementary treatment of bifurcations.

John Stensby, Professor Electrical and Computer EngineeringReviews: 4. Buy Topics in Bifurcation Theory and Applications on FREE SHIPPING on qualified orders Topics in Bifurcation Theory and Applications: Iooss, Gerard, Adelmeyer, Moritz: : Books.

These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner. Nonlinear Stability and Bifurcation Theory Book Subtitle An Introduction for Engineers and Applied Scientists / Softcover ISBN.

Bifurcation theory states that oscillations in a dynamic system begin and end at certain critical points in the system. As mentioned above, the Z. mobilis fermentation process demonstrates static and dynamic bifurcation behaviors over a wide range of operating parameters.

Therefore, we must elucidate the distribution of Hopf points in this system. 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 s: 2. In its most general form bifurcation theory is a theory of equilibrium solutions of nonlinear equations.

By equilibrium 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.

For plastic bifurcation analysis of plates and shells, the paradox still remains that the analytically more rigorous flow theory usually produces bifurcation buckling loads which agree less closely with experimental results and are higher than those from a deformation theory analysis (Teng, ).It is generally accepted that a bifurcation analysis based on the deformation theory provides a.

Topics in stability and bifurcation theory. Berlin ; New York: Springer-Verlag, (DLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: David H Sattinger. 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.

Most of the expository material consists of a concise presentation of basic results and problems in structural stability. The most significant contribution of the book is the formulation of structural stability and bifurcation in infinite dimensions.

Much research should come from this—indeed some have already picked up the ideas in their work. Elementary Stability and Bifurcation Theory Hardcover – 2 December particularly if you aren't a math major who has had a few advanced mathematics topics such as partial differential equations, vector calculus etc previously.

There is a clear dearth of examples in this book and the symbols make the subject quite s: 2. 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. 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. 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.

It is generally believed that the mathematical theory of bifurcation requires some functional analysis and some of the methods of topology and dynamics. Schaeffer D.G.

() Topics in Bifurcation Theory. In: Ball J.M. (eds) Systems of Nonlinear Partial Differential Equations. NATO Science Series C: (closed) (Mathematical and Physical Sciences (Continued Within NATO Science Series II: Mathematics, Physics and Chemistry)), vol. The stability and nonexistence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution with the changes of a specific parameter are obtained by analyzing the distribution of the.Fundamentals of bifurcation theory and stability analysis.

October ; In book: Modelling of instabilities and bifurcation in Geomechanics It aims at providing the basic ideas of bifur.This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems.