For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises.
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Text: English (translation)
Original Language: Dutch
Original Language: Dutch
From the Back Cover
On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed first. Stability theory is then developed starting with linearisation methods going back to Lyapunov and Poincaré. In the last four chapters more advanced topics like relaxation oscillations, bifurcation theory, chaos in mappings and differential equations, Hamiltonian systems are introduced, leading up to the frontiers of current research: thus the reader can start to work on open research problems, after studying this book. This new edition contains an extensive analysis of fractal sets with dynamical aspects like the correlation- and information dimension. In Hamiltonian systems, topics like Birkhoff normal forms and the Poincaré-Birkhoff theorem on periodic solutions have been added. There are now 6 appendices with new material on invariant manifolds, bifurcation of strongly nonlinear self-excited systems and normal forms of Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, and is illustrated by many examples.
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7 of 9 people found the following review helpful:
3.0 out of 5 stars
Springer dropped the ball,
By G. Cantor "Base three" (Mill Valley, CA USA) - See all my reviews
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This review is from: Nonlinear Differential Equations and Dynamical Systems (Universitext) (Paperback)
Over all, Verhulst does a ressonable job of conveying the central ideas of the topic. I found it to be slow going for a couple of reasons: First, it's clearly a translation and Springer should have done a better proofreading job ... many of the sentence constructions are unusual for English which is, at the very least, distracting. Second, there are substantial gaps in some of the arguments ... maybe ok for a book at this level, but it often creates considerable frustration.In contrast, the book by Jordan and Smith (Nonlinear Ordinary Differential Equations) has few flaws and, in my view, should be read first.
5.0 out of 5 stars
This book takes you by hand through dynamical systems theory,
This review is from: Nonlinear Differential Equations and Dynamical Systems (Universitext) (Paperback)
What I like more of this work is tha the autor explains all theconcepts he is using, so it is ideal for people who is a naturalscientist but not necesarilly knows all the formalism of modern mathematics. It is not hard to read and covers the basics for study recent research papers. END
1 of 3 people found the following review helpful:
5.0 out of 5 stars
This book takes you by hand through dynamical systems theory,
This review is from: Nonlinear Differential Equations and Dynamical Systems (Universitext) (Paperback)
What I like more of this work is tha the autor explains all theconcepts he is using, so it is ideal for people who is a naturalscientist but not necesarilly knows all the formalism of modern mathematics. It is not hard to read and covers the basics for study recent research papers. END
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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Citations (learn more)
66
books
cite this book:
See all 66 books citing this book
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- Theory and Numerics of Differential Equations by James F. Blowey in Back Matter
- Issues of Fault Diagnosis for Dynamic Systems by Ron J. Patton in Back Matter
- Abstract Linear Algebra (Universitext) by Morton L. Curtis in Front Matter
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