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＜E-Book＞
The Center and Cyclicity Problems : A Computational Algebra Approach / by Valery Romanovski, Douglas Shafer

Edition	1st ed. 2009.
Publisher	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
Year	2009
Language	English
Size	XII, 330 p. 4 illus : online resource
Authors	*Romanovski, Valery author Shafer, Douglas author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Differential equations LCSH:Algebraic fields LCSH:Polynomials LCSH:Algebra LCSH:Mathematics -- Data processing  All Subject Search FREE:Dynamical Systems FREE:Differential Equations FREE:Field Theory and Polynomials FREE:Algebra FREE:Computational Mathematics and Numerical Analysis
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-0-8176-4727-8

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