《非線性振動、動力學系統和矢量場的分叉》是2018年世界圖書出版公司出版的著作，作者是[美] J.古肯海默，P.霍姆斯。
基本介紹
- 中文名：非線性振動、動力學系統和矢量場的分叉
- 作者：[美] J.古肯海默，P.霍姆斯
- 出版時間：2018年01月01日
- 出版社：世界圖書出版公司
- ISBN：9787519226176
- 定價：世界圖書出版公司
- 開本：16 開
- 裝幀：平裝
內容簡介,作者簡介,目錄,
內容簡介
本書是論述動力學系統、分叉理論與非線性振動研究之間接口部分的理論專著，主要討論以歐氏空間微分流形為相空間，以及常微分方程組和映象集為數學模型的問題。本書初版於1983年，本版是2002第7次修訂版，該書出版三十餘年來倍受讀者歡迎，是混沌動力學的經典教材。
作者簡介
John. Guckenheimer（J.古肯海默）是美國康奈爾大學數學系教授，Philip. Holmes（P.霍姆斯）是美國普林斯頓大學教授。
目錄
CHAPTER 1
Introduction： Differential Equations and Dynamical Systems
1.1 Existence and Uniqueness of Solutions
1.1 The Linear System x = Ax
1.2 Flows and Invariant Subspaces
1.3 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
1.9 Peixoto's Theorem for Two-Dimensional Flows
CHAPTER 2
An Introduction to Chaos： Four Examples
2.1 Van der Pol's Equation
2.2 Duffing's Equaiion
2.3 The Lorenz Equations
2.4 The Dynamics of a Bouncing Ball
2.5 Conclusions： The Moral of the Tales
CHAPTER 3
Local Bifurcations
3.1 BiFurcation Problems
3.2 Center Manifolds
3.3 Normal Forms
3.4 Codimension One Bifurcations of Equilibria
3.5 Codimension One Bifurcations of Maps 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 and Local Bifurcations
4.4 Averaging， Hamikonian Systems， and Global Behavior： Cautionary Notes
4.5 Melnikov's Method： Perturbations of Planar Homoclinic Orbits
4.6 Melnikov's Method： Perturbations of Hamiltonian Systems and Subharmonic Orbits
4.7 Stability or 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 of a Hyperbolic Limit Set
5.2 Invariant Sets and Hyperbolicity
5.3 Markov Partitions and Symbolic Dynamics
5.4 Strange Auractors 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 Properties： Dimension， Entropy， and Liapunov Exponents
CHAPTER 6
Global Bifurcations
6.1 Saddle Connections
6.2 Rotation Numbers
6.3 Bifurcations or One-Dimensional Maps
6.4 The Lorenz Bifurcations
6.5 Homoclinic Orbits in Three-Dimensional Flows： Silnikov's Example
6.6 Homoclinic aifurcations of Periodic Orbits
6.7 Wild Hyperbolic Sets
68 Renormalization and Universality
CHAPTER 7
Local Codimension Two Bifurcations of Flows
7.1 Degeneracy in Higher-Order Terms
7.2 A Note on k-Jets 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 Applicaiions to Large Systems
APPENDIX
Suggestions for Further Reading
Postscript Added at Second Printing
Glossary
References
Index
