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 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
This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms.
From the reviews:
"Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
This volume is intended for advanced undergraduate, graduates and researchers as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas which will enable students to take specific dynamical systems and obtain some quantitative information about the behaviour of these systems. The new edition has been updated and extended throughout and contains an extensive bibliography as well as a detailed glossary of terms.