The center and cyclicity problems: a computational approach

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 ofdynamical systems and families of polynomial systems. The text first lays thegroundwork for computational algebra and gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on thetheory 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. Each chapter includesexamples, exercises, algorithms and historical notes The computational algebra approach provides additional understanding of the center and cyclicity problems Includes foundational material on the center and cyclicity problems as well as current research efforts INDICE: Preface.- 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.- References.- Index.

• ISBN: 978-0-8176-4726-1
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 300
• Fecha Publicación: 01/09/2008
• Nº Volúmenes: 1
• Idioma: Inglés