Hilbertʹs 16-th problem for quadratic vector fields and cyclicity of graphics Original Research Article

We discuss here a method of proof of the existential part of Hilbertʹs 16th problem for quadratic vector fields initiated in 1991 [7]. The program consists in proving the finite cyclicity of 121 graphics appearing among quadratic systems. We briefly summarize some of the methods introduced for that purpose and describe some new developments obtained with Świrszcz and Żoldek [20] for graphics surrounding a center.