Bifurcation of limit cycles near equivariant compound cycles  

作　　者：Mao-an HAN Tong-hua ZHANG Hong ZANG 

机构地区：[1]Department of Mathematics,Shanghai Normal University,Shanghai 200234,China

出　　处：《Science China Mathematics》2007年第4期503-514,共12页中国科学：数学（英文版）

基　　金：The work was supported by the National Natural Science Foundation of China (Grant No. 10671127);Program for New Century Excellent Talents in University (Grant No. NCET-04-0388)

摘　　要：In this paper we study some equivariant systems on the plane. We first give some criteria for the outer or inner stability of compound cycles of these systems. Then we investigate the number of limit cycles which appear near a compound cycle of a Hamiltonian equivariant system under equivariant perturbations. In the last part of the paper we present an application of our general theory to show that a Z3 equivariant system can have 13 limit cycles.In this paper we study some equivariant systems on the plane. We first give some criteria for the outer or inner stability of compound cycles of these systems. Then we investigate the number of limit cycles which appear near a compound cycle of a Hamiltonian equivariant system under equivariant perturbations. In the last part of the paper we present an application of our general theory to show that a Z 3 equivariant system can have 13 limit cycles.

关 键 词：equivariant system STABILITY BIFURCATION limit cycle 34C05 34G10 58F11 

分 类 号：O192[理学—数学]