Geometric Configurations of Singularities of Planar Polynomial Differential Systems: A Global Classification in the Quadratic Case

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.