Differential Equations, Dynamical Systems, and Linear Algebra

1st Edition

Authors: Morris W. Hirsch Stephen Smale Robert L. Devaney Stephen Smale
Hardcover ISBN: 9780123495501
eBook ISBN: 9780080873763
Imprint: Academic Press
Published Date: 28th April 1974
Page Count: 358
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Description

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

Readership

Advanced undergraduate and graduate students studying mathematics.

Table of Contents

Preface. First Examples. Newton's Equation and Kepler's Law. Linear Systems with Constant Coeffecients and Real Eigenvalues. Linear Systems with Constant Coefficients and Complex Eigenvalues. Linear Systems and Exponentials of Operators. Linear Systems and Canonical Forms of Operators. Contractions and Generic Properties of Operators. Fundamental Theory. Stability of Equilibria. Differential Equations for Electrical Circuits. The Poincare-Bendixson Theorem. Ecology. Periodic Attractors. Classical Mechanics. Nonautonomous Equations and Differentiability of Flows. Perturbation Theory and Structural Stability. Elementary Facts. Polynomials. On Canonical Forms. The Inverse Function Theorem. References. Answers to Selected Problems. Index.

Details

No. of pages:
358
Language:
English
Copyright:
© Academic Press 1974
Published:
Imprint:
Academic Press
eBook ISBN:
9780080873763
Hardcover ISBN:
9780123495501

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

Stephen Smale

Affiliations and Expertise

University of California, Berkeley, USA

Reviews

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.