Cyclicity of elementary polycycles and ensembles with codimension 3 degeneration

The conjecture E(k)less than or equal to k is proved to be true if and only if k=1, 2, 3, where E(k) is the cyclicity of condimension k generic elemen tary polycycles. It is also proved that the cyclicity of any codimension 3 ensembles except ensembles with "lips" is less than or equal to 6. By the w ay, the methods usually used in the study of cyclicity of polycycles such a s derivation division algorithm, Khovanskii procedure and the method of cri tical point analysis are introduced.