Rev. ed. of: Differential equations, dynamical systems, and linear algebra / Morris W. Hirsch and Stephen Smale. 1974.

Includes bibliographical references (p. 407-409) and index.

Preface First Order Equations Planar Linear Systems Phase Portraits for Planar Systems Classification of Planar Systems Higher Dimensional Linear Algebra Higher Dimensional Linear Systems Nonlinear Systems Equilibria in Nonlinear Systems Global Nonlinear Techniques 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

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. It is developed by award-winning researchers and authors. It provides a rigorous yet accessible introduction to differential equations and dynamical systems. It includes bifurcation theory throughout and contains numerous explorations for students to embark upon. It includes new contemporary material and updated applications. It contains revisions throughout the text, including simplification of many theorem hypotheses. It features: many new figures and illustrations; simplified treatment of linear algebra; detailed discussion of the chaotic behavior in the Lorenz attractor; the Shil'nikov systems; the double scroll attractor; and, increased coverage of discrete dynamical systems.