Using a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research reference.
Publisher: Birkhauser Boston Inc
Number of pages: 330
Weight: 1080 g
Dimensions: 235 x 155 x 18 mm
Edition: 2009 ed.
From the reviews:
"This book treats in detail the problem of computing the center conditions and the cyclicity ... . The book is written very clearly and ... entirely self-contained. This makes it quite approachable for beginning researchers as well as a reference for those who know the area well. ... furnished with a large number of exercises and examples, together with pseudo-code for the computations. An appendix gives some of these routines in Mathematica. Altogether an ideal book for those wishing to start research in this area." (Colin J. Christopher, Mathematical Reviews, Issue 2010 h)
"The primary object in this interesting book is to study small-amplitude periodic solutions of planar polynomial autonomous systems which concerns the Poincare center (center-focus) problem and the cyclicity problem (the local 16th Hilbert problem). ... the book is designed for the use as a primary textbook in an advanced graduate course ... . The book is of interest not only for those working in the field of differential equations, but also for researches from the field of computational algebra and symbolic computation ... ." (Alexander Grin, Zentralblatt MATH, Vol. 1192, 2010)