Abstract
Our main objective is to explore the shape and geometry of the limiting curves of the structures that define the escape properties of a particle from a lobular domain in a multiwell potential. For this purpose, we examine the lower umbilical catastrophe [Formula: see text], for [Formula: see text], by calculating the Lyapunov orbit at the entrance of the lobular region as well as the set of incoming asymptotic trajectories to it and the set of successive intersections of this set with a proper surface of section.
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