Overview
Presents novel, powerful tools for studying algebraic bifurcations in quadratic differential systems
Introduces an algebra software package that will allow readers to avoid complicated calculations once they have understood the main concepts
Provides methods that are highly useful for studying several large families of quadratic systems and for checking classifications made with classical tools, as well as revealing some flaws in them
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Table of contents (13 chapters)
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Front Matter
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Polynomial differential systems with emphasis on the quadratic ones
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Front Matter
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Configurations of singularities of quadratic systems
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Front Matter
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Back Matter
Keywords
About this book
This book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones.
The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors’ results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming.
Given its scope, the book will appeal to specialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.
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Authors and Affiliations
About the authors
Jaume Llibre is Full Professor at the Departament de Matemàtiques, Universitat Autònoma de Barcelona in Barcelona, Spain.
Dana Schlomiuk is Honorary Professor, former Full Professor at the Département de Mathématiques et de Statistiques, Université de Montréal in Montreal, Canada.
Nicolae Vulpe is Professor, Principal Researcher at the Vladimir Andrunachievici Institute of Mathematics and Computer Science in Chisinau, Moldova.
Bibliographic Information
Book Title: Geometric Configurations of Singularities of Planar Polynomial Differential Systems
Book Subtitle: A Global Classification in the Quadratic Case
Authors: Joan C. Artés, Jaume Llibre, Dana Schlomiuk, Nicolae Vulpe
DOI: https://doi.org/10.1007/978-3-030-50570-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-50569-1Published: 18 June 2021
Softcover ISBN: 978-3-030-50572-1Published: 19 June 2022
eBook ISBN: 978-3-030-50570-7Published: 17 June 2021
Edition Number: 1
Number of Pages: XII, 699
Topics: Global Analysis and Analysis on Manifolds, Ordinary Differential Equations