Cyclicity of planar polycycles and ensembles with codimension 3 degeneration through a saddle-node and two hyperbolic saddles

The cyclicity of four classes of codimension 3 plnnar polycycles and ensembles containing a saddle-node and two hyperbdic saddles is dealt with. The exnct cyclicity or cyclicity bound of them is obtained by finitely-smooth normal form theory.

The cyclicity of four classes of codimension 3 planar polycycles and ensembles containing a saddle node and two hyperbolic saddles is dealt with. The exact cyclicity or cyclicity bound of them is obtained by finitely smooth normal form theory.