Geometric Configurations of Singularities of Planar Polynomial Differential Systems
A Global Classification in the Quadratic Case
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Beschreibung
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 tospecialists 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.
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.
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
Autor*in
Joan C. Artés
Themen in »Geometric Configurations of Singularities of Planar Polynomial Differential Systems«
quadratic vector fields infinite and finite singularities affine invariant polynomials Poincaré compactification configuration of singularities geometric equivalence relation ordinary differential equations
Stimmen zu »Geometric Configurations of Singularities of Planar Polynomial Differential Systems«
“This excellent book is a survey of results in the qualitative study of real planar quadratic differential systems, a significant part of which was derived by the authors themselves, who are outstanding researchers in this field. … The book ends with an extensive bibliography concerning various aspects of the topic of the presented research results. This survey will be very useful for the interested reader.” (Alexander Grin, zbMATH 1493.37001, 2022)
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