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 ex...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.展开更多
文摘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.
