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Synopsis
Although this systematic study of autonomous systems begins with a thorough treatment of linear systems, the main emphasis is on local and global behavior of nonlinear systems. The main purpose of this revised edition is to introduce students to the qualitative and geometric theory of ordinary differential equations as well as serving as a reference book for mathematicians researching dynamical systems. Readers will find that, except for certain topics of current mathematical research, such as the number of limit cycles and the nature of attracting sets of dynamical systems, the global qualitative theory of a nonlinear dynamical system leads to an understanding of the solution set of the nonlinear system to rival that which we have of linear flows.
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From the Back Cover
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 Poincare 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 contains materials on higher order Melnikov functions 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.
Review
Reviews from the first edition:
“...The text succeeds admiraby ... Examples abound, figures are used to advantage, and a reasonable balance is maintained between what is proved in detail and what is asserted with supporting references ... Each section closes with a set of problems, many of which are quite interesting and round out the text material ... this book is to be highly recommended both for use as a text, and for professionals in other fields wanting to gain insight into modern aspects of the geometric theory of continuous (i.e., not discrete) dynamical systems.” MATHEMATICAL REVIEWS
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- PublisherSpringer
- Publication date1993
- ISBN 10 0387974431
- ISBN 13 9780387974439
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages407
- Rating
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Differential Equations and Dynamical Systems (Texts in Applied Mathematics)
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Differential Equations and Dynamical Systems (Texts in Applied Mathematics)
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Differential Equations and Dynamical Systems
Published by
Springer-Verlag, New York, 1993
ISBN 10: 0387974431
ISBN 13: 9780387974439
Used
Hardcover
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hardcover. Condition: as new. no jacket. 6 1/4 x 9 1/2 " 403 pages. Texts In Applied Mathematics 7. Seller Inventory # 116821
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Differential Equations and Dynamical Systems
Published by
New York : Springer-Verlag, 1991
ISBN 10: 0387974431
ISBN 13: 9780387974439
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Condition: Good. Original boards, illustrated with numerous equations, graphs and diagrams, 8vo. Texts in Applied Mathematics, volume 7.; Name in pen on title page, spine discoloured, back cover partly discoloured. Seller Inventory # 341002-ZA16
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Differential Equations and Dynamical Systems. ( = Texts in Applied Mathematics, 7).
Seller: Antiquariat Silvanus - Inhaber Johannes Schaefer, Ahrbrück, Germany
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Second corrected printing,. 407 pp. with 177 Illustrations, 0387974431 Sprache: Englisch Gewicht in Gramm: 740 Groß 8°, Original-Pappband (Hardcover), Rücken leicht aufgehellt, insgesamt sehr gutes und innen sauberes Exemplar, Seller Inventory # 80175
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Differential Equations and Dynamical Systems (Texts in Applied Mathematics)
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Differential Equations and Dynamical Systems (Texts in Applied Mathematics 7)
Published by
Springer-Verlag, New York, 1991
ISBN 10: 0387974431
ISBN 13: 9780387974439
Used
Hardcover
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Hardcover. Condition: Very Good. New York, Berlin, London et al: Springer Verlag, 1991. 9 1/2 x 6 1/4 inches: pp. xii, 403, Glossy yellow boards with black boards. Some light scuffing, scratches to boards. Previous owner's embossed stamp, with no ink, on upper corner of free facing end page. Text is unmarked. Binding tight. Seller Inventory # 4431973
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Differential Equations and Dynamical Systems (Texts in Applied Mathematics, Vol 7)
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