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25 Remote Warehouse Mathematics- Popular Chaos and Fractals

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields Cover

 

Synopses & Reviews

Publisher Comments:

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

Synopsis:

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their 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 readers develop an intuitive feel for the properties involved.

Description:

Bibliography: p. 437-454.

Table of Contents

Chapter 1: Introduction: Differential Equations and Dynamical Systems * Chapter 2: An Introduction to Chaos: Four Examples * Chapter 3: Local Bifurcations * Chapter 4: Averaging and Perturbation from a Geometric Viewpoint * Chapter 5: Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors * Chapter 6: Global Bifurcations * Chapter 7: Local Codimension Two Bifurcations of Flows * Appendix * Suggestions for Further Reading * Postscript Added at Second Printing * Glossary * References * Index

Product Details

ISBN:
9780387908199
Editor:
John, F.
Editor:
Marsden, Jerrold E.
Author:
Guckenheimer, J.
Author:
Holmes, Philip
Author:
Guckenheimer, John
Author:
Marsden, Jerrold E.
Publisher:
Springer
Location:
New York, NY
Subject:
Differential Equations
Subject:
Mathematical Analysis
Subject:
Chaotic Behavior in Systems
Subject:
Differentiable dynamical systems
Subject:
Oscillations
Subject:
Nonlinear oscillations
Subject:
Bifurcation theory
Subject:
Vector fields.
Subject:
Fields
Subject:
Dynamische Systeme
Subject:
Bifurcations
Subject:
Verzweigung (Math.)
Subject:
Chaos (Math.)
Subject:
Nichtlineare Schwingung
Subject:
Seltsamer Attraktor
Subject:
Vector
Subject:
Analysis
Subject:
Mathematics-Popular Chaos and Fractals
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Copyright:
Edition Number:
3
Edition Description:
1983. Corr. 6th
Series:
Applied Mathematical Sciences
Series Volume:
42
Publication Date:
19830801
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
484
Dimensions:
235 x 155 mm 1880 gr

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Related Subjects

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Science and Mathematics » Mathematics » Analysis General
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Science and Mathematics » Mathematics » Popular Chaos and Fractals
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields New Hardcover
0 stars - 0 reviews
$140.25 In Stock
Product details 484 pages Springer-Verlag - English 9780387908199 Reviews:
"Synopsis" by , An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their 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 readers develop an intuitive feel for the properties involved.
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