|Title||The Center and Cyclicity Problems: A Computational Algebra Approach|
|Author(s)|| V.G. Romanovskii, D.S. Shafer|
|Type||Book, Chapter in Book, Conference Proceeding|
|Abstract||In the last three decades, new methods for investigating polynomial ideals and their varieties have emerged, providing new possibilities for approaching the long-standing center and cyclicity problems. Using a computational algebra approach, this work addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems.|
The text first lays the groundwork for computational algebra and 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. The center and cyclicity problems are then explored in detail.
Containing exercises as well as historical notes and algorithms, this self-contained text is suitable for an advanced graduate course in the subject as well as a reference for researchers.},
|Keywords||bifurcations, limit cycles, normal forms, stability, computer algebra|