Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems.

Audience
Advanced students and practitioners in higher mathematics.

Contents

• First-Order Equations
• Planar Linear Systems
• Phase Portraits for Planar Systems
• Classification of Planar Systems
• Higher Dimensional Linear Systems
• Nonlinear Systems
• Equilibria in Nonlinear Systems
• Global Nonlinear Systems
• Closed Orbits and Limit Sets
• Applications in Biology
• Applications in Circuit Theory
• Applications in Mechanics
• The Lorenz System
• Discrete Dynamical Systems
• Homoclinic Phenomena
• Existence and Uniqueness Revisited