Introduction to Applied Nonlinear Dynamical Systems and Chaos
Introduction to Applied Nonlinear Dynamical Systems and Chaos
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DOI：
10.2307/3620310
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发表时间：
1989-10
期刊：
影响因子：
--
通讯作者：
S. Wiggins
中科院分区：
文献类型：
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作者：
S. Wiggins
平衡解、稳定性和线性化稳定性* Liapunov函数*不变流形：线性和非线性系统*周期轨道*具有积分的向量场*指标理论*向量场的一些一般性质：存在性、唯一性、可微性和流性*渐近性* Poincare- bendixson定理* Poincare映射*映射的共轭性和变截面*结构稳定性、一般性和横向性*拉格朗日方程*哈密顿向量场*梯度向量场*可逆动力系统*渐近自治向量场*中心流形*正规形式*向量场不动点的分岔*映射不动点的分岔*关于分岔图的解释和应用警告的话*小马掌*符号动力学* Conley-Moser条件或“如何证明一个动力系统是混沌的”*二维映射的同斜点附近的动力学*轨道同斜到三维自治向量场中的双曲不动点* Melnikov在二维时间周期向量场中的同斜轨道的方法* Liapunov指数*混沌和奇异吸引子*双曲不变集：一个混沌鞍*耗散系统中的长周期汇和保守系统中的椭圆岛*局部余维二分岔引起的全局分岔*常用术语词汇
Equilibrium Solutions, Stability, and Linearized Stability * Liapunov Functions * Invariant Manifolds: Linear and Nonlinear Systems * Periodic Orbits * Vector Fields Possessing an Integral * Index Theory * Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows * Asymptotic Behavior * The Poincare-Bendixson Theorem * Poincare Maps * Conjugacies of Maps, and Varying the Cross-Section * Structural Stability, Genericity, and Transversality * Lagrange's Equations * Hamiltonian Vector Fields * Gradient Vector Fields * Reversible Dynamical Systems * Asymptotically Autonomous Vector Fields * Center Manifolds * Normal Forms * Bifurcation of Fixed Points of Vector Fields * Bifurcations of Fixed Points of Maps * On the Interpretation and Application of Bifurcation Diagrams: A Word of Caution * The Smale Horseshoe * Symbolic Dynamics * The Conley-Moser Conditions or 'How to Prove That a Dynamical System is Chaotic' * Dynamics Near Homoclinic Points of Two-Dimensional Maps * Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields * Melnikov's Method for Homoclinic Orbits in Two-Dimensional, Time-Periodic Vector Fields * Liapunov Exponents * Chaos and Strange Attractors * Hyperbolic Invariant Sets: A Chaotic Saddle * Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems * Global Bifurcations Arising from Local Codimension-Two Bifurcations * Glossary of Frequently Used Terms