Differential Equations, Dynamical Systems, and an Introduction to Chaos

Differential Equations, Dynamical Systems, and an Introduction to Chaos

2nd Edition - October 22, 2003

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  • Authors: Morris W. Hirsch, Stephen Smale, Robert L. Devaney
  • eBook ISBN: 9780080491141

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Description

Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems. The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems. This book will be particularly useful to advanced students and practitioners in higher mathematics.

Key Features

  • Developed by award-winning researchers and authors
  • Provides a rigorous yet accessible introduction to differential equations and dynamical systems
  • Includes bifurcation theory throughout
  • Contains numerous explorations for students to embark upon

NEW IN THIS EDITION

  • New contemporary material and updated applications
  • Revisions throughout the text, including simplification of many theorem hypotheses
  • Many new figures and illustrations
  • Simplified treatment of linear algebra
  • Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor
  • Increased coverage of discrete dynamical systems

Readership

Advanced students and practitioners in higher mathematics

Table of Contents

  • 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

Product details

  • No. of pages: 425
  • Language: English
  • Copyright: © Academic Press 2003
  • Published: October 22, 2003
  • Imprint: Academic Press
  • eBook ISBN: 9780080491141

About the Authors

Morris W. Hirsch

Affiliations and Expertise

University of Wisconsin, Madison, USA

Stephen Smale

Affiliations and Expertise

University of California, Berkeley, USA

Robert L. Devaney

Affiliations and Expertise

Boston University, MA, USA

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