Perturbations from a kind of quartic Hamiltonians under general cubic polynomials  

作　　者：ZHAO LiQin WANG Qi 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University and Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,China [2]Department of Mathematics,College of Science,Hebei University of Science and Technology,Shijiazhuang 050018,China

出　　处：《Science China Mathematics》2009年第3期427-442,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10671020)

摘　　要：In this paper we investigate the perturbations from a kind of quartic Hamiltonians under general cubic polynomials. It is proved that the number of isolated zeros of the related abelian integrals around only one center is not more than 12 except the case of global center. It is also proved that there exists a cubic polynomial such that the disturbed vector field has at least 3 limit cycles while the corresponding vector field without perturbations belongs to the saddle loop case.In this paper we investigate the perturbations from a kind of quartic Hamiltonians under general cubic polynomials. It is proved that the number of isolated zeros of the related abelian integrals around only one center is not more than 12 except the case of global center. It is also proved that there exists a cubic polynomial such that the disturbed vector field has at least 3 limit cycles while the corresponding vector field without perturbations belongs to the saddle loop case.

关 键 词：abelian integral elliptic Hamiltonian homoclinic bifurcation 58F14 58F21 58F30 34C05 

分 类 号：O175[理学—数学]