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Introduction to Applied Nonlinear Dynamical Systems and Chaos

This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative...

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Bibliographic Details
Main Author: Wiggins, Stephen. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic
Language:English
Published: New York, NY : Springer New York, 2003.
Edition:Second Edition.
Series:Texts in Applied Mathematics, 2
Subjects:
Mathematics.
Dynamics.
Ergodic theory.
Applied mathematics.
Engineering mathematics.
Statistical physics.
Dynamical systems.
Dynamical Systems and Ergodic Theory.
Applications of Mathematics.
Statistical Physics, Dynamical Systems and Complexity.
Appl.Mathematics/Computational Methods of Engineering.
Online Access:View fulltext via EzAccess
Table of Contents:
  • 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 Poincaré-Bendixson Theorem
  • Poincaré Maps
  • Conjugacies of Maps, and Varying the Cross-Section
  • Structural Stability, Genericity, and Transversality
  • LagrangéƠ"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 ́ƠSHow to Prove That a Dynamical System is ChaotićƠý
  • Dynamics Near Homoclinic Points of Two-Dimensional Maps
  • Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields
  • Melnikov́Ơs 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 CodimensiońƠ Two Bifurcations
  • Glossary of Frequently Used Terms.

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