具有双中心的三次可积非Hamiltonian系统的Poincaré分支  

The Poincaré Bifurcation of Cubic Non-Hamiltonian Integrable Systems with Double Centers

作　　者：宋燕[1] 

机构地区：[1]渤海大学数学系,辽宁锦州121000

出　　处：《工程数学学报》2008年第4期679-684,共6页Chinese Journal of Engineering Mathematics

摘　　要：本文讨论一类具有双中心的三次可积非Hamiltonian系统的Poincaré分支问题,此问题的证明可归结为Abel积分的零点个数估计。利用Picard-Fuchs方程和Riccati方程讨论系统轨线的性态,证明其Poincaré分支最多可以产生6个极限环,而且可以产生6个极限环。In this paper, we study the Poincaré bifurcation of cubic non-Hamiltonian integrable systems with double centers. The proof relies on an estimation of the number of zeros of a related Abelian integrals. By using the Picard-Fuchs equation and the Riccati equation, we derive the properties of trajectory and prove that the Poincaré bifurcation may and can generate six limit cycles after a small cubic perturbation.

关 键 词：三次可积非Hamiltonian系统 POINCARÉ分支 PICARD-FUCHS方程 极限环 ABEL积分 

分 类 号：O175[理学—数学]