Cyclicity of Degenerate Polycycles Through a Saddle-Node and Two Hyperbolic Saddles

This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle.node and two hyperbolic saddles, where the hyperbolicity ratio of the saddle (which connects the saddle.node with hp.connection) is equal to 1 and that of the other saddle is irrational. It is obtained that the cyclicity of this kind of polycycle is no more than 5 if the hp.connection keeps unbroken under the C. perturbations.