Geometric Configurations of Singularities of Planar Polynomial Differential Systems

Joan C. Artés is Associate Professor at the Departament de Matemàtiques, Universitat Autònoma de Barcelona in Barcelona, Spain.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.

“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)

• Part I.- Polynomial differential systems with emphasis on the quadratic ones.- 1 Introduction.- 2 Survey of results on quadratic differential systems.- 3 Singularities of polynomial differential systems.- 4 Invariants in mathematical classification problems.- 5 Invariant theory of planar polynomial vector fields.- 6 Main results on classifications of singularities in QS.- 7 Classifications of quadratic systems with special singularities.- Part II.- 8 QS with finite singularities of total multiplicity at most one.- 9 QS with finite singularities of total multiplicity two.- 10 QS with finite singularities of total multiplicity three.- 11 QS with finite singularities of total multiplicity four.- 12 Degenerate quadratic systems.- 13 Conclusions.