Introduction to Applied Nonlinear Dynamical Systems and Chaos (Hardcover, 2, 2003)

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