A family of critical curves that lie in the range of a class of Poincaré halfmaps induced by a saddle focus in three-space is investigated analytically. It comprises all "far final points" of the images of invariant curves that are subject to a separating mechanism. The number of branches occurring on a specific critical curve is directly related to the type of separating mechanism present in the halfmap. Moreover, universal properties of the saddle-focus dynamics are demonstrated for the first time.
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