多角环的环性及二次系统的Hilbert16问题

In this project we mainly investigate the cyclicity of planar polycycles through two hyperbolic saddles and one saddle-node under some degenerate conditions. It is obtained that the cyclicity of this kind of polycycle is finite. As an application, we obtain that the cyclicity of one kind of polycycle which is the limit periodic set of quatratic systems has finite cyclicity under the same degenerate conditions.

本项目研究二次系统极限周期集的121种多角环非孤立环的有限环性问题。欧美学者将二次低臣藁犯鍪囊恢掠薪缧晕侍饣拗芷诩?21种多角环的有限环问题。半数以上的孤立初等环已解决。非孤立初等环的有限环性是遗留问题中难点之一。本项目将致力于解决此问题。它是沿着此途径解决二次系统的Hilbert 第16问题的关键之一。.