Structurally unstable quadratic vector fields of codimension one [ Back ]

15:30 to 16:30
UAB - Dept. Matemàtiques (C1/-128)
Joan Carles Artés
Universitat Autònoma de Barcelona


In 1998 Llibre and me, with the collaboration of Robert Kooij from Delft published a Memoirs of AMS on "Structurally unstable quadratic vector fields" where it was proved that there are exactly 44 different phase portraits modulo limit cycles.
Just after ending that work we engaged in a much more challenging task of finding all "Structurally unstable quadratic vector fields of codimension one" also modulo limit cycles, as a next step towards a complete classification of all quadratic systems.
We have found (in collaboration with Alex Rezende from Brazil) that there are at least 204 different phase portaits in this class and no more than 211.
The reason we have lasted 20 years in completing this step is that we have needed to create some new tools to study quadratic systems and study some big families in order to obtain many needed examples.
With some newly obtained results on higher codimensions, the final goal becomes achievable in some middle term.