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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.

The Center and Cyclicity Problems: A Computational Algebra Approach

Polynomial Ideals and Their Varieties.- Stability and Normal Forms.- The Center Problem.- The Isochronicity and Linearizability Problems.- Invariants of the Rotation Group.- Bifurcations of Limit Cycles and Critical Periods.