抛物线边界二次系统单中心环域的Poincaré分支

Poincaré bifurcation for quadratic systems with a bound of parabola and a single center

主要利用Picard-Fuchs方程和Riccati方程法,解决了一类以抛物线为边界的单中心环域可积非Hamilton系统在二次多项式扰动下的Poincaré分支问题,得出此系统的Poincaré分支最多可以扰动出三个极限环。

The work of this thesis mainly focuses on the non -Hamilton integral system with quadratic perturbations . A class of Poincare＇ bifurcation systems with a bound of parabola and a single center is solved using Picard -Fuchs equation and Riccati equation, so we get this system at most exist 3 limit cycles with perturbation.