非线性振动,动力学系统和矢量场的分叉

《非线性振动，动力学系统和矢量场的分叉》是1999年世界图书出版公司出版的图书，作者是J.Guckenheimer例请统状等。

• 作者 J.Guckenheimer / 等
• ISBN 9787506214711
• 页数 459
• 定价 73.00元
• 出版社 世界图书出版公司

内容介绍

　　Pr来自oblems in dynamics have fascinated physical scientists (and mankind in general) for thousands of years. Notable among such problems are those of celestia360百科l mechanic棉病画八四s, especia封黄lly the study of the motions of the bodies in t因烈回代扩庆he solar system. Newton's attempts to understand and model their observed motions incorporated Kepler's laws and led to his development of the calculus. With this the study of models of dynamical problems as differential equations began.

　　本书为英文火希版。

作品目录

　　Contents

　　CHAPTE拿耐切R1

　　Introduction: Differential Equations and Dynamical Systems

　　1.0. Existence and Uniqueness ofSolutions

　　1.1. The Linear System x = Ax

价罗危感众　　1.2. Flows and Invariant Subspaces

　　1.3承民民使卫度. The Nonlinear System x = f(x)

　　1.4. Linear and Nonlinear Maps

　　1.5. Closed Orbits. Poincare Maps and Forced Oscillations

　　1.6. Asymptotic Behavior

　　1.7. Equivalence Relations and Structural Stability

　　1.8. Two-Dimensional Flows

　　1支二异伤.9. Peixoto's Theore内抓不帮孩义m for Two-Dimensional Flows

　　CHAPTER 2

　　An Introduction to 现半夫止末Chaos: Four Examples

　　2.1. Van 艺成娘响斗香限年der Pol's Equation

　　2.2. Duffing's Equation

　　2.3. The Lorenz Equations

　　2.4. The Dynamics ofa Bouncing Ball

　　2.5. Conclusions: The Moral ofthe Tales

　　CHAPTER 3

　　Local Bifurcations

　　3.1. Bifurcation Problems

　收识齐某理　3.2. Cent行言迫洋温见称沿事er Manifolds

　　3.3. Normal Forms

　　3.4. Codimension One Bifurcations of Equilibria

　　3.纸发载块音言括问5. Codimension One Bifurcations ofMaps and Periodic Orbits

　　CHAPTER 4

　　Averaging and Perturbation from a Geometric Viewpoint

　　4.1. Averaging and Poincare Maps

　　4.2. Examples of Averaging

　　4.3. Averaging 白字参何维军案脱的损and Local Bifureations

　　4.4. Averaging, Hamiltonian Systems, and Global Behavior:

　　Cautionary Notes

　　4.5. Melnikov's Method: Perturbations ofPlanar Homoclinic O少策西守地直般环威套门rbits

　　4.6. Melnikov's Method: Perturbations of Hamiltonian Systems and

　　Subharm米影务十onic Orbit论今s

　　4.7. Stability of Subharmonic Orbits

　　4.8. Two Degree of Freedom Hamiltonians and Area Preserving Maps

　　of the Plane

　　CHAPTER 5

　　Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors

　　5.0. Introduction

　　5.1. The Smale Horseshoe: An Example ofa Hyperbolic Limit Set

　　5.2. Invariant Sets and Hyperbolicity

　　5.3. Markov Partitions and Symbolic Dynamics

　　5.4. Strange Attractors and the Stability Dogma

　　5.5. Structurally Stable Attractors

　　5.6. One-Dimensional Evidence for Strange Attractors

　　5.7. The Geometric Lorenz Attractor

　　5.8. Statistical Propenies: Dimension. Entropy and Liapunov Exponents

　　CHAPTER 6

　　Global Bifurcations

　　6.1. Saddle Connections

　　6.2. Rotation Numbers

　　6.3. Bifurcations of One-Dimensional Maps

　　6.4. The Lorenz Bifurcations

　　6.5. Homoclinic Orbits in Three-Dimensional Flows: Silnikov's Example

　　6.6. Homoclinic Bifurcations of Periodic Orbits

　　6.7. Wild Hyperbolic Sets

　　6.8. Renormalization and Universality

　　CHAPTER7

　　Local Codimension Two Bifurcations of Flows

　　7.1. Degeneracy in Higher-Order Terms

　　7.2. A Note on k-Sels and Determinacy

　　7.3. The Double Zero Eigenvalue

　　7.4. A Pure Imaginary Pair and a Simple Zero Eigenvalue

　　7.5. Two Pure Imaginary Pairs of Eigenvalues without Resonance

　　7.6. Applications to Large Systems

　　APPENDIX

　　Suggestions for Further Reading

　　Postscript Added at Second Printing

　　Glossary

　　References

　　Index