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Field name	Details
Dewey Class	515.39 (DDC 23)
Title	The Center and Cyclicity Problems ([Ebook]) : A Computational Algebra Approach / by Douglas Shafer, Valery Romanovski.
Author	Shafer, Douglas
Added Personal Name	Romanovski, Valery
Other name(s)	SpringerLink (Online service)
Publication	Boston : Birkhäuser , 2009.
Physical Details	: online resource.
ISBN	9780817647278
Summary Note	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 PoincarÃ© 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.:
Contents note	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.
System details note	Online Access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-4727-8
Links to Related Works	Subject References: Algebra . Computational Mathematics and Numerical Analysis . Computer Science . Differentiable dynamical systems . Differential equation . Differential equations, Partial . Dynamical systems and ergodic theory . Field Theory and Polynomials . Field theory (Physics) . Partial differential equations . Authors: author . Romanovski, Valery . Shafer, Douglas . Corporate Authors: SpringerLink (Online service) . Classification: 515.39 (DDC 23) .

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The Center and Cyclicity Problems: A Computational Algebra Approach

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