Main description:
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.
- 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
Review quote:
"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
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
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.
- 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
Review quote:
"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
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