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Differential Equations and Dynamical Systems
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Binding: Hardcover
Dewey Decimal Number: 515.353
EAN: 9780387951164
Edition: 3rd
ISBN: 0387951164
Label: Springer
Manufacturer: Springer
Number Of Items: 1
Number Of Pages: 568
Publication Date: April 01, 2006
Publisher: Springer
Studio: Springer
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Editorial Review:
This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincaré map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.
Customer Reviews
Average Rating: 
Rating: - Very good graduate ODEs text, with some flaws
Perko's book is one of the best books that gives an advanced introduction to dynamical systems from the point of differential equations. Many other good books tread the same ground, without emphasizing the connection to ODEs. Perko's text is particularly strong in several respects. First, the dynamical systems it considers are almost always expressed in terms of underlying differential equations. Second, it gives proofs or outlines of proofs of most major theorems used in this field. Third, ... Read More
Rating: - A Book on Advanced Dynamical Systems
This book is a useful textbook for advanced courses on differential equations and dynamical systems for senior undergraduate students or first year graduate students.
The book presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems.
The book has a sketch of the proof of the Hartman-Grobman Theorem which was useful for my second undergraduate course on dynamical systems and nonlinear differential equations.
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