Cyclicity of elementary polycycles and ensembles with codimension 3 degeneration  

作　　者：Liqin Zhao Weigu Li Zhifen Zhang 

机构地区：[1]Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China [2]Peking Univ, Dept Math, Beijing 100871, Peoples R China

出　　处：《Chinese Science Bulletin》1998年第22期1849-1864,共16页

基　　金：theNationalNaturalScienceFoundationofChina (GrantNo .197710 0 7);theDoctoralProgramFoundationofInstitutionofHigherEducationofChina (GrantNo.96 0 0 0 15 4 )

摘　　要：The conjecture E(k)≤k is proved to be true if and only if k=1, 2, 3, where E(k) is the cyclicity of condimension k generic elementary polycycles. It is also proved that the cyclicity of any codimension 3 ensembles except ensembles with "lips" is ≤6. By the way, the methods usually used in the study of cyclicity of polycycles such as derivation division algorithm, Khovanskii procedure and the method of critical point analysis are introduced.The conjectureE(k)?k is proved to be true if and only ifk=1, 2, 3, whereE(k) is the cyclicity of condimensionk generic elementary polycycles. It is also proved that the cyclicity of any codimension 3 ensembles except ensembles with “lips” is ?6. By the way, the methods usually used in the study of cyclicity of polycycles such as derivation division algorithm, Khovanskii procedure and the method of critical point analysis are introduced.

关 键 词：POLYCYCLE CYCLICITY finitely_smooth normal form Dulac map 

分 类 号：O176.3[理学—数学]