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The Center and Cyclicity Problems: A Computational Algebra Approach - Softcover

 
9780817647261: The Center and Cyclicity Problems: A Computational Algebra Approach

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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.

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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.

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  • PublisherBirkhäuser
  • Publication date2009
  • ISBN 10 0817647260
  • ISBN 13 9780817647261
  • BindingPaperback
  • LanguageEnglish
  • Number of pages342

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Kartoniert / Broschiert. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Each chapter includes examples, exercises, algorithms and historical notesThe computational algebra approach provides additional understanding of the center and cyclicity problemsIncludes foundational material on the center and cyclicity pr. Seller Inventory # 5975873

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Taschenbuch. Condition: Neu. 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. Seller Inventory # 9780817647261

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