Differential Equations, Dynamical Systems, and an Introduction to Chaos - 2nd Edition - ISBN: 9780123497031, 9780080491141

Differential Equations, Dynamical Systems, and an Introduction to Chaos

2nd Edition

Authors: Morris W. Hirsch Stephen Smale Robert L. Devaney Morris W. Hirsch Robert L. Devaney
eBook ISBN: 9780080491141
Imprint: Academic Press
Published Date: 22nd October 2003
Page Count: 425
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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

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

Details

No. of pages:
425
Language:
English
Copyright:
© Academic Press 2004
Published:
Imprint:
Academic Press
eBook ISBN:
9780080491141

About the Author

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

Morris W. Hirsch

Affiliations and Expertise

University of Wisconsin, Madison, USA

Robert L. Devaney

Affiliations and Expertise

Boston University, MA, USA

Reviews

"The exposition is excellent. I particularly liked how the proofs are fairly easy to follow... There are several instances where 'What if...?' questions come up naturally and the authors explore these as though they were reading your mind." - Gareth Roberts, Holy Cross "This text contains exactly what a student entering graduate school in Dynamical Systems needs to know; it is Dynamical Systems from three mathematicians who are not only among the world's most prominent experts in dynamical systems, but who are also among the world's best mathematical expositors. The book contains the benchmark models of chaos to which much of current research is compared" - Bruce Peckham, University of Minnesota "The presentation is very clear and often supported by carefully selected key-examples. The book meets very high pedagogical standards and certainly is a worthy successor of the original version." -R. Steinbauer, Wien, in MONATSHEFTE FUR MATHEMATIC, VOL 147