The Center and Cyclicity Problems : A Computational Algebra Approach

Valery Romanovski

ISBN 10: 0817647260 / ISBN 13: 9780817647261

Editore: Birkhauser Boston Apr 2009, 2009

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Neuware - In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: the Poincaré center problem and the cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories).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; this isfollowed by a discussionregarding the theory of normal forms and stability of differential equations. The center and cyclicity problems are then explored in detail.The book contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography. Completely self-contained, it is thus suitablemainly as a textbook for a graduate course in the subject but also as a reference for researchers. Codice articolo 9780817647261

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Titolo: The Center and Cyclicity Problems : A ...

Casa editrice: Birkhauser Boston Apr 2009

Data di pubblicazione: 2009

Legatura: Taschenbuch

Condizione: Neu

Descrizione articolo

Riassunto:

Using a computational algebra approach, this work addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The self-contained text contains exercises as well as historical notes and algorithms.

Dalla quarta di copertina:

In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: the Poincaré center problem and the cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories).

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; this is followed by a discussion regarding the theory of normal forms and stability of differential equations. The center and cyclicity problems are then explored in detail.

The book contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography. Completely self-contained, it is thus suitable mainly as a textbook for a graduate course in the subject but also as a reference for researchers.