Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit "chaotic behavior." The first portion of the book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms and the logistic map and area-preserving planar maps. The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder. The text contains many worked examples and exercises, many with hints. It will be a valuable first textbook for senior undergraduate and postgraduate students of mathematics, physics, and engineering.
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||||||||
Book Description
Frequently Bought Together
Editorial Reviews
Review
"...a very good textbook. It brings the reader in a short time through the fundamental ideas underlying the theory of dynamical systems theory." Mathematical Reviews
"...a good textbook on the subject." Physics in Canada
"...a true introduction to the modern theory of dynamical systems....It has many clear figures and it has copious exercises which were readily solvable and instructive." Kenneth R. Meyer, SIAM Review
"...a good textbook on the subject." Physics in Canada
"...a true introduction to the modern theory of dynamical systems....It has many clear figures and it has copious exercises which were readily solvable and instructive." Kenneth R. Meyer, SIAM Review
Book Description
Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit "chaotic behavior".
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
6 of 7 people found the following review helpful:
5.0 out of 5 stars
Excellent Introduction to the Subject,
By Michael Raghib (Bogota Colombia) - See all my reviews
This review is from: An Introduction to Dynamical Systems (Paperback)
covers most important areas of the subject with a clear yet rigorous approach. Advanced text better suited for graduate students in applied math. It promises as a must for anyone serious about the subject
6 of 7 people found the following review helpful:
5.0 out of 5 stars
Excellent focus on what is important,
By A Customer
This review is from: An Introduction to Dynamical Systems (Paperback)
Dynamical systems is a vast subject to which no single book can provide an adequate introduction, but the authors do an excellent job of focusing on what is important and avoiding the temptation to go off on enticing tangents. Their treatment is clear, and this book is highly recommended for any student seeking a solid foundation for further work.
Share your thoughts with other customers: Create your own review
|
|
Inside This Book
(learn more)
First Sentence:
A dynamical system is one whose state changes with time (t). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
vector field approximation, hyperbolic invariant circle, hyperbolic linear diffeomorphisms, additional resonance term, elliptic periodic points, horseshoe diffeomorphism, normal form calculations, bifurcational behaviour, dissipative twist maps, linear flow exp, infinity jet, planar diffeomorphisms, dissipative standard map, structurally stable flows, complex normal form, transverse homoclinic points, versal unfolding, trapping hypothesis, homoclinic saddle connection, topological behaviour, twist homeomorphism, canonical polar, transformed vector field, local phase portrait, hyperbolic saddle point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Implicit Function Theorem, Hartman Theorem, Hartman's Theorem, Denjoy's Theorem, Classical Mechanics New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A dynamical system is one whose state changes with time (t). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
vector field approximation, hyperbolic invariant circle, hyperbolic linear diffeomorphisms, additional resonance term, elliptic periodic points, horseshoe diffeomorphism, normal form calculations, bifurcational behaviour, dissipative twist maps, linear flow exp, infinity jet, planar diffeomorphisms, dissipative standard map, structurally stable flows, complex normal form, transverse homoclinic points, versal unfolding, trapping hypothesis, homoclinic saddle connection, topological behaviour, twist homeomorphism, canonical polar, transformed vector field, local phase portrait, hyperbolic saddle point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Implicit Function Theorem, Hartman Theorem, Hartman's Theorem, Denjoy's Theorem, Classical Mechanics New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 31
books:
See all 31 books this book cites
67
books
cite this book:
See all 67 books citing this book
- Chaotic Behaviour of Deterministic Systems (Ecole D'ete De Physique Theoretique Les Houches//Proceedings) by G. Iooss in Back Matter (1), and Back Matter (2)
- Ordinary Differential Equations by Garrett Birkhoff in Back Matter (1), and Back Matter (2)
- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Back Matter
- The Second Scientific American Book of Mathematical Puzzles and Diversions by Martin Gardner in Back Matter
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Back Matter
See all 31 books this book cites
- Stochastically Excited Nonlinear Ocean Structures by Michael F. Shlesinger on page 211, and page 223
- Mathematical Methods and Models for Economists by Angel de la Fuente on page 455, and page 491
- Nonlinear Control and Analytical Mechanics: A Computational Approach (Control Engineering) by Harry G. Kwatny on page 16, and page 35
- Nonlinearity in Structural Dynamics: Detection, Identification and Modelling by K Worden in Back Matter
- Nonlinear Mathematics and its Applications: Proceedings of the EPSRC Postgraduate Spring School in Applied Nonlinear Mathematics, University of Surrey, 1995 by Philip J. Aston on page 43
See all 67 books citing this book
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Suggested Tags from Similar Products(What's this?)Be the first one to add a relevant tag (keyword that's strongly related to this product).
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
