Finite Cyclicity of HH-graphics with a Triple Nilpotent Singularity of Codimension 3 or 4

Series: 
CDSNS Colloquium
Monday, February 17, 2014 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
School of Mathematics, Georgia Institute of Technology
 In 1994, Dumortier, Roussarie and Rousseau launched a program aiming at proving the finiteness part of Hilbert’s 16th problem for the quadratic system. For the program, 121 graphics need to be proved to have finite cyclicity. In this presentation, I will show that 4 families of HH-graphics with a triple nilpotent singularity of saddle or elliptic type have finite cyclicity. Finishing the proof of the cyclicity of these 4 families of HH-graphics represents one important step towards the proof of the finiteness part of Hilbert’s 16th problem for quadratic systems. This is a joint work with Professor Christiane Rousseau and Professor Huaiping Zhu.