About this book
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.
- Book Title Differential Equations and Dynamical Systems
- Series Title Texts in Applied Mathematics
- DOI https://doi.org/10.1007/978-1-4613-0003-8
- Copyright Information Springer-Verlag New York 2001
- Publisher Name Springer, New York, NY
- eBook Packages Springer Book Archive
- Hardcover ISBN 978-0-387-95116-4
- Softcover ISBN 978-1-4612-6526-9
- eBook ISBN 978-1-4613-0003-8
- Series ISSN 0939-2475
- Series E-ISSN 2196-9949
- Edition Number 3
- Number of Pages XIV, 557
- Number of Illustrations 11 b/w illustrations, 0 illustrations in colour
Fluid- and Aerodynamics
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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