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eBay-Artikelnr.:267248715022
Artikelmerkmale
- Artikelzustand
- Pages
- 462
- Publication Date
- 1983-08-01
- Book Title
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Ve
- Edition Number
- 3
- ISBN
- 9780387908199
Über dieses Produkt
Product Identifiers
Publisher
Springer New York
ISBN-10
0387908196
ISBN-13
9780387908199
eBay Product ID (ePID)
154682
Product Key Features
Number of Pages
Xvi, 462 Pages
Language
English
Publication Name
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Subject
Differential Equations / General, Mathematical Analysis
Publication Year
1983
Features
Reprint
Type
Textbook
Subject Area
Mathematics
Series
Applied Mathematical Sciences Ser.
Format
Hardcover
Dimensions
Item Height
0.4 in
Item Weight
66.3 Oz
Item Length
9.2 in
Item Width
6.1 in
Additional Product Features
Edition Number
3
Intended Audience
Scholarly & Professional
LCCN
97-135723
Dewey Edition
21
Reviews
J. Guckenheimer and P. Holmes Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields "The book is rewarding reading . . . The elementary chapters are suitable for an introductory graduate course for mathematicians and physicists . . . Its excellent survey of the mathematical literature makes it a valuable reference."-JOURNAL OF STATISTICAL PHYSICS, J. Guckenheimer and P. Holmes Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields "The book is rewarding reading . . . The elementary chapters are suitable for an introductory graduate course for mathematicians and physicists . . . Its excellent survey of the mathematical literature makes it a valuable reference."--JOURNAL OF STATISTICAL PHYSICS, J. Guckenheimer and P. HolmesNonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields"The book is rewarding reading . . . The elementary chapters are suitable for an introductory graduate course for mathematicians and physicists . . . Its excellent survey of the mathematical literature makes it a valuable reference."-JOURNAL OF STATISTICAL PHYSICS
Series Volume Number
42
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
510 s
Edition Description
Reprint
Table Of Content
Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.
Synopsis
This book applied the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking the cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help the reader develop an intuitive feel for the properties involved., From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." # Book Review - Engineering Societies Library, New York #1 "An attempt to make research tools concerning strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." # American Mathematical Monthly #2, From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." # Book Review - Engineering Societies Library, New York #1 "An attempt to make research tools concerning 'strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." # American Mathematical Monthly #2
LC Classification Number
QA299.6-433
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